OK, as others have said, a 'point and shoot' film camera is usually the name given to one of the compact autofocus and auto exposure type 35mm film cameras with built in flash, such as this one, the Canon Sureshot Supreme:
Last time I looked, this model camera was still quite good value for money (around £20 upwards for one in good working order) and have a good, sharp lens on them, if you can put up with the retro plastic and slightly banana-shaped looks, and there's no way to focus manually or set the shutter speed or aperture manually either.
However, I think what you are referring to might be an auto exposure, manual focus, 35mm SLR? If so, neither the OM10 or AE1 are truly
full auto exposure... each require either the shutter speed or the aperture to be set by the photographer, and the camera then choses the other setting according to what the camera's light meter tells it.
The Canon A1 does give full auto exposure (Programme),choosing both the shutter speed and aperture automatically. It also offers full manual, as well as setting the shutter speed or aperture automatically, while the photographer sets the other. It was the first 35mm SLR camera to offer the now familiar PASM exposure settings that virtually all DSLRs still have to this day.
Unless prices have changed since last time I looked, the Canon A1 tends to sell for a bit less than the AE1 and AE1 programme, although the A1 is a much higher specification camera! I think this is because the other two are silver and black and look more retro. So if you want the camera for photography rather than posing, the A1 wins hands down for specification and value for money.
However, the Canon A series cameras are
manual focus only, and use the old Canon FD fit lenses (modern Canon EOS EF and EF-S fit lenses
wont fit or work on them). If you want a more modern auto-focus 35mm SLR (that you can just point at the subject and press the shutter) then perhaps have a look at a Canon EOS 30. This was one of the last of the 35mm film cameras and is quite high spec but still sells for reasonable money. It will work fully with all Canon EF lenses (
not the EF-S fit lenses though!) and current and recent Canon Speedlite flash guns too (EX 430 and EX 430II).
So it depends what you want, but I doubt you can go far wrong with either the A1 or EOS 30 providing you get a fully working one with a warranty from a reputable shop/dealership. Buying privately from an internet auction site can be a bit more of a lottery and camera repairs aren't cheap if it does go wrong.
Above all,
don't rush into buying, there are loads of cameras out there, so make sure you are going to buy the right one for you! Hope this is useful.
Have a look at the 'Film and Conventional' forum section of Talk Photography too, lots of experienced folk in there, together with info on film and where to get your film developed and scanned too. Nice friendly people too.