there's really no need for the AC adapter plug computer fans mostly run on DC but all those old cell phone charger and things you have laying around with those big annoying brick like plugs, all those bricks are power converters to change AC to DC so you could do like i did and just cut the wire to that and use that and presto u have DC for free. some people use Computer power supplies i feel like that's way overkill just to run fans on. the way your thinking about doing it is fine but this can save you a few bucks and you can wire in a rheostat this way which from my understanding is kind of important. it was stressed to me that i use one by a few people.
i added that florescent light in there two just an 18 inch under cabinet florescent light fixture for 10 bucks from home depot i seen them at walmart for 7 right after i bought it too. and i grabbed a blacklight bulb as you can see i thought it would be cool to see the eggs glow XD, but the light is putting off a good amount of its own heat so idk if im going to be able to let it run 24/7 without messing with the temps =/