Err.. time to back up I think.... WHY do you want to try film? What do you hope to achieve? What 'difference' you you hope to experience shooting film to widgetal?
At the most basic level, there's not a heck of a lot of difference... it's just what is behind the lens to catch the light... silver halide or a silicon chip. The rest is all the same. A-N-D, the modern DSLR is actually an evolution of the last-of-the-line Auto-Focus film cameras, just with a silicon chip where the silver halide film would have gone, and are little different to use, other than having to chuck a film in them and go to the chemists to get pictures to look at off it!
Film-Format... again, most simply, 'large format cameras' take a picture on a 'plate'. Conventionally this was a piece of window glass, 10x8 inch square, for 'full-plate' but could be 'half plate', 8x5" or quarter-plate, 4x5", but since advent of celluloid, the 'plate' is replaced with 'cut-sheet' film.
Medium-Format.... conventionally is a camera that uses a celuloid 'roll'film',, most often 6cm wide 120 roll-film, that will give a number of frames per-roll. How many depends on how the frame is orientated along or across the film. Frame sizes on 120, conventionally, are 4.5x6cm 'accross' the film, or 6x6cm square on the film, or 6x9cm 'along' the film.
35mm is 'small-format' and conventionally make a frame 24x36mm square on the film. But like Medium format, you can play with the frame size you put on that film. 'Half-Frame' 35mm cameras like the Olympus Pen, use the film 'side-ways' to make a 24x16mm frame on it; co-incidentally the same size as was originally conceived for 35mm in movie cameras, the film was developed for, as well as for APS format cameras, that evolved into the APS-C sensor size for digital... But 'Small-Format; encompasses a range of film-sizes like the 220 cartridge film, that are smaller than 120 roll film, but bigger than 'miniature' formats.
Miniature format film... most popular probably the 110 cartridge, which puts a 13.x17mm frame on the film, but again, includes a range of film sizes and alternative frame sizes, most often based on 16mm film stock. Beneath those..... you get into sub-miniature formats, like the Minox spy camera that makes a tiny 10x8mm frame on its diddy little film.
A-N-D..... that's as far as it goes. It's 'just' the size of film behind the lens, little else... so why do you want to use film, and is it aactually the film that atracts you or the usually lesser level or....
AUTOMATION - This is where the biggest differences are to be found. Mentioned the last of the line Auto-Focus SLR film cameras, being little different to the early digital DSLR's, and in fact the earliest of them were based on 35mm or APS film cameras, literally with little difference but a silicon chip where the film would have gone....
Earlier film SLR's like my humble Zenit, were completely 'manual'. There was virtually NO automation or easement in the things, so you had to meter the scene's brightness, either by eye, f-16 Sunny style, or with a hand-held meter. Decide by guess-work and or experience, or from the pictorial guide on the film packet, or a set of tables, maybe a computer 'wheel' oft built into a hand-held meter, what shutter-speed, what aperture settings to select for the film sped you had and the brightness of the scene.... then focus the lens manually, either by eye through the viewfinder if an SLR or twin-lens-reflex' or by scale, either with a helpful range-finder to help you guess the distance, that again might have been built into the camera or an accessory, or a bit of guess-work and or experience to a scale on the lens, or more 'broadly' to some icons for 'near' 'middle' and 'far' distant subjects (Zone focus).
Later, and probably the majority of 35mm Film SLR's, had in-built ';Through-Taking-Lens' light meters. My Zenit has no meter at all, I have to use a Hand-Held meter. My Sigma, on the other hand has an in-built TTL meter, that shows a hi/lo swing needle in the view-finder. This is actually 'coupled' and shifts the center depending on the ASA/Shutter/Aperture settings I have made, but I still have to make them all 'manually'. My OM10, on the other hand is fully 'Auto-Exposure, and I have to set the film-speed and aperture manually, but the shutter-speed is coupled to the TTL light-meter, and sets the shutter speed to balence the meter against the other 'settings'.
On a modern DSLR.... you may pretty much turn off or on as much or as little of the automation as you want, or dont want, and if you turn 'off' the auto-focus, and turn the exposure mode to 'manual'.... you pretty much have something that works like my old Sigma 35mm SLR fil camera. So how 'involved' do you want top get, and how much automation do you want NOT to have? And is 'film' really doing anything you want for you?
PROCESSING - Something you cant really replicate in widgetal, is taking the film out the camera, putting it in a day-light tank, mixing chemicals, and bathing the film according to a recipe on the bottles or in a book, then taking the film out and seeing the pictures you took... probably in negative..... but developing to the recipe, it's actually NOT all 'that' much more engaging than taking the film to Boots to do for you..... but, presuming negative film, next step is to make a positive 'print', which used to beg an enlarger to blow up the negative image to the size of a piece of paper, that you then has to develop like the film... lots and lots of stuff to do, its very involved and very interesting and making your own prints does give you loads and loads of 'control' of how the picture you see gets to be a picture you can hang on the wall.....
THIS is the most significant departure using film to widgetal.... you have to get messy with chemicals to make the picture happen... is THAT what you want to do?
In which case "What Camera" is pretty irrelevant; do you want to develop and print black and white? Do you want to tackle colour? What bits of processing would you like to experiment with or explore? Different development processes and brews? Different printing techniques, like dodging and burning, or multiple image montaging? WHERE do you hope to take it?
Now, I started home-processing in the early 90's, because I didn't feel I was doing 'all' I could in this photography lark, just pointing the camera. Plus it was getting expensive, and home developing slide film looked like a good way to save pennies. I then bought a second hand enlarger, and had a crack at first developing and printing Black and White, which is all pretty do-able and good fun, before trying to tackle colour... which isn't! But, I discovered a 'scanner' at work, and had a mess with what was then known as "Digital Dark-Room' on the computer.... could do much the same things as I could in the dark room, in both colour and B&W and not have to make so much mess!
Back to what you hope to experience from film..... shooting an all auto film camera isn't much different to shooting a DSLR; getting film commercially developed, is little different, just more expensive than taking an SD card out the camera, and putting film through the scanner to play in Photo-Shop is not really doing much different, to shooting direct-to-digital....
NOW... I mostly shoot 35mm film... and I probably put as much film through my beloved Olympus XA2 'compact', or Konica C35 'range-finder', as I do either my Sigma SLR or my OM10 SLR.... I do have an OM4, but I have sort of given up on the ruddy thing since the batteries went flat on frame 12, when both new film and new batteries were fitted at the same time! I also have a 120 Roll-film, Ziess Ikonta 'folder' and a Voiglander TLR. which are pertinent...
I DON'T use the MF cameras mostly because they are a pain in the bum. The film is incredibly expensive, and on the Ikonta particularly I only get 10 frames a roll! The image quality, IS however superb...... B-U-T... it don't fit in my scanner.... and even of it did.... shrunk to 1000pixels on the long-side for screen-view and web-load! RATHER wasted on any-one, unless I made prints.... BIG prints!
Which was pretty much my conclusion over 1/4 century ago, when I was loaned a Hassablad, Medium Format, 6x6 SLR. I actually went to the camera shop and bought some, Ilford B&W of the same emulsion in 120 and 35mm and shot a range of subjects back-to-back, with the 'Blad, my OM4, and my XA2...... and after a Christmas break off work, in the dark-room, and a LOT of wasted printing paper.... my conclusion was, that I could barely see blugger all difference, especially until I was making tiny sectional enlargements of the frame at huge magnifications and looking at them under a magnifying glass..... sort of old-skool pixel peeping!
Don't get me wrong.... the Ziess Ikonta is a lovely camera to use. All manual, its very involving, B-U-T... to all practical extents and purposes, I don't get anything 'more' from it than I do my old Sigma Mk1... its just as tactile and mechanical and involving... with the convenience of that exposure meter in the view-finder, and possibility of interchangeable prime lenses....
And SO!!!! We get down closer to the nitty gritty of your question......
The world of 'film' cameras is huge. And immediately, I have mentioned my Olympus XA2 compact. Fantastic camera, one of the smallest full-frame 35mm film cameras ever made, delivering SLR rivaling image quality from a pretty sophisticated (for the time!) Auto-Exposure system, making it pretty much point and press friendly. The Konica was my Grandad's, and slightly earlier than the XA2, it was like the XA2 NOT a 'cheap' camera, but with an automatic exposure system, as well as a rather good 'true' focal length lens, did serve up SLR rivaling results from something that was pretty P&S friendly, with some degree of 'manual' over-ride control on that if wanted. But there are loads of old non SLR film cameras about like this, and JUST because they aren't an SLR they can be a real steal in the 2nd hand market, these days. In the 120 Medium-Format world, there's a similar trend. That Ziess Ikonta folder of mine, was another family heirloom, but e-bay value is probably something rather less than £25, mostly because its not an iconic Miyama or Bronica 'interchangeable lens' camera.
If you are a 'bit' savvy about what you are about, and what you really want to do, or experience, there are an ENORMOUSE number of old film cameras out there, you could pick from, in either 35mm or Medium-Format, with as much 'manual', or 'little' manual involvement as you want.
I will pick the my Sigma as an example. its 35mm, so it uses reletively cheap, common, available and easily manages film stock. I can drop a film in to ASDA and have a one hour procesing on it in the time it takes me to choose what bread to buy, not have to send it to a specialist or pay a fortune for it. It fits my scanner, and I can make digi-files as good or as quick as I need to most purposes, or probably better. If I shoot B&W I can play chemicals at home, and again, scan or print, and play as much or little as I want. The camera is 'involving' to use, demanding I make my own settings to the swing needle, but doesn't demand I work entirely to guess work or wave a hand-held meter about. Machine-Gun 'Ker-Chunk' of the shutter, and the stiff resistance of the controls, including the focus, is all very nice and lets me 'feel' like I am actually doing stuff... and the image quality is more than good enough for most purposes, far better than needed for web-display, certainly more than enough for prints up to 10x8 inches.... So the merit of MF is pretty marginal. On the other hand? The 'convenience' of the XA2 is fantastic, as it has been for the last 40 years.... also unobtrusive, and yeah, NOT so 'engaging', but not really the point of the thing, which is to let me concentrate on finding and composing scenes.
So.... back to the question... WHAT do you want to do with a film camera? What are you hoping to experience?
The camera really matters very little, its whether that choice will deliver what you hope for.... And you can spend as little or as much as you want really, before during or after picking film....
PERSONALLY I would suggest, as a toe-in-the-water, exercise, you start 35mm. Its cheap-er, its more available, and so much more accessible than MF.
I would guess that you want an SLR. because that's the 'done' thing and you feel like you have a camera in your hand for it. But, do you really want or need interchangeable lenses? And if so, zooms or primes? The at a touch re-framing of a zoom, is much like the automation, all too easy to expect and exploit and NOT get that engagement or involvement or 'experience' having to work with the fixed framing of a prime.... and there, if you force yourself to work with a restricted range of primes? Do you really need interchangeable lenses? Would a fixed lens range-finder or zone-focus camera be 'as' demanding and involved to use?
Its all lots of choices, and they all depend on your aspirations and expectations; there's no one-sized-fits all off the peg answer here.
And if you just want to take pictures, that you are going to get commercially developed, and printed, and maybe scanned.... are you really getting anything at all from film.... think long and hard..... the film is as important as the camera, what you do with the film after its been through the camera the same.
What camera is but TINY part of the over-all question here..... 35mm vs MF?!? Even smaller part.....
Diving in without giving some thought to the bigger picture, you are setting up either for mistakes and regrets and or disappointment, and possibly a lot of unnecessary expense. Giving it a bit of thought, identifying what you really hope to get from film? You stand a much better chance of picking something more suitable and getting a lot more from it, and it probably wont matter an awful lot WHAT the actual camera happens to be.
Back to you, I think!