A 10 to 20 gal tank sounds good but what I do is feed them in another container. Chopped fish, reptomin, etc and then I clean it out when I get home from work. It keeps the main tank much cleaner for a longer period. A heat lamp and a fairly warm room would be best. I think a good diet is more important than lighting. I've had musk turtles reach 3 inches in 2 years using regular aquarium fluorescent bulbs.
Good luck.