Hi Andy. The D3300 will do TTL flash - either using the pop-up in auto mode, or using Nikon CLS compatible flash units. As you've already realised it does not support using the pop-up as a flash commander though, so for remote TTL you'll need either a CLS master capable flash mounted on the camera or a dedicated TTL controller like the old Nikon SU-800, or a 3rd party radio system like the Yongnuo YN622 or Godox X1-T I use the Yongnuo 622 system for my Nikon cameras and SB900 flashes and it works well, however the Godox family is much more integrated - their big flashes use the same radio system. If I was buying small flash today, I'd go for the Godox system. You could buy a curly cable that connects to the hotshoe and provides a remote hotshoe on the other end, but tbh, radio triggers are so cheap now there's not very much point. I do have one, but I got it to put the *master* flash somewhere else to better talk to the remotes - in the days before reasonable priced radio TTL systems like the YN622.
Now - to answer your question about flash versus continuous, we need to get them into common units. Continuous lights (lets say a tungsten light for the sake of this comparison) may be rated at say 1kiloWatt. This means it will consume 1KJoule of energy every second (1Watt is one Joule per second), and output a portion of that as light (and the rest mainly as heat). I'm not going to get into the exact efficiency of the light here as you'll see in a few seconds that the difference is so huge that it doesn't really matter, so lets assume 1kWatt of light is produced. Now lets consider a typical flashgun like the Nikon SB900. It holds and delivers about 70 Joules of light on max power, in about 1/900th of a second (just over a millisecond). Power is "work" or energy delivered over time so 70 Joules divided by 1/900th of a second = 70x900 or roughly 63 kiloWatts. So the speed-light is 63 times as *powerful* as a 1kW continuous light. Note I'm using these terms correctly here - power is the rate of delivery, not the amount delivered - you'll often hear flashes described as a "500 Watt" flash. What they really mean is 500 Watt-seconds or 500 Joules of energy is delivered in total. So as the speed-light is 63 times as powerful, but only for 1/900th of a second, we need to specify a time period - ie a shutter speed for the continuous light (it doesn't really matter for the flash - as long as the shutter is open completely at some point, it will get its light out). In order to get the same 70 joules of light out, the 1 kWatt (1000 Joules per second) continuous light must shine for 70/1000 or 7/100 or ~ 1/15th of second - assuming everything else remains the same (ISO, Aperture). 1/15th of a second may not seem very long, but unless your subject remains very still, and so do you, your shots may very well be blurred, and that's a for a 1kiloWatt tungsten - that's quite beefy for a continuous light.
In summary - flash is much much more powerful than continuous lights, and it's this immense power that enables us to set exposures on our cameras so that only the flash is powerful enough to even show up. In this way we can replace the ambient light with light of our own design - without having to start in a totally dark room.
The Godox TT685-N
http://flashhavoc.com/godox-tt685n-ttl-speedlight-released/ is probably the best all-round 3rd party speed-light for Nikon today coupled with their X1T-N radio controller and trigger, as the same trigger will operate the rest of the Godox range. I like this deal I found
on ebay for 2 TT685 plus an X1T-N trigger and 2 Bowens S compatible mounts (a nice robust way of supporting a flash on a light stand with the added bonus of enabling use of S-Fit modifiers):-
http://www.ebay.co.uk/itm/UK-2-Godo...084347&hash=item3ad299e119:g:OoQAAOSw4GVYLqN4
It is also available with with a proprietary Lithium battery as the V860-IIN. This will no doubt last longer than a set of NiMh rechargeable batteries and will recycle faster, however it is a proprietary battery, and yet another charger. This version also loses the external power connector (for really fast recycle times), and is about 50% more expensive than the TT685.
Now of course you don't *need* TTL for indoor, controlled portraits and product shots - but it's nice to have for other use cases. You'll also need some stands, and I'd recommend a small softbox like this one:-
http://www.ebay.co.uk/itm/Neewer-24...055008&hash=item2caa3475e5:g:E~IAAOSw2gxYz4IM
and maybe a shoot-through and reflective brolly
http://www.ebay.co.uk/itm/Photo-Stu...002881?hash=item2cbfc64441:g:ZF4AAOSwxg5Xzo1a
http://www.ebay.co.uk/itm/85cm-Umbr...146868?hash=item5b39775934:g:r5UAAOSw42dZNUUj
and a pop-up reflector. I like these Lencarta ones with a handle that also have a standard screw thread for a lighting spigot (so you can mount it directly to a light stand):-
https://www.lencarta.com/56cm-redline-pro-handheld-folding-reflector
