offer them some land or a log to bask in. Babies are a little touchy with water parameters so use some reptile dechlor zoo med makes one that is very good. Feed live for the first few months to get an appetite going then offer frozen fish crab anything for that matter... they eat anything and everything that fits in their mouths. Good luck and be prepared for a long lasting pet that gets huge !
Alligators are a little easier, but way bigger. Check out turtleman.com, they have info and they are the best source of CB snappers, as well as the leucistic morph.
If you can manage, an outdoor, murky pond is best. They WILL go on land, contrary to popular belief. But its no big deal if you dont, its just a something you should do if its not too far out of your way.
I think an alligator snapper is one of those pets where if you have it, you'll probably be more satisfied keeping it in an aquarium where you can actually see it rather than in a murky pond outside. They don't seem like the kind of turtles that will swim up to you in hopes of being fed like common snappers will, but I've never had one so I don't know.