Ditto to the crested gecko suggestion. They're very simple to care for... Don't need extra heat, as their ideal temp range is between about 72 and 76. Anything over 80 can actually make them ill.
They don't need live food... They actually thrive on a prepared diet, Crested Gecko Diet by Repashy, which is a powder that you mix with water to make into a paste. Change that out every other day, add crickets once a week or so if you feel like it, and they're good.
Humidity is the big thing... They do need to be kept very humid. They are also big time climbers, but that's just another plus for it being a standard 20 gallon--it has plenty of climbing space.
So, my suggestion would be a Crested Gecko, or another smaller Rhacodactylus or related gecko. i.e. Gargoyle geckos. A couple great forums for Cresteds and similar geckos are
http://forums.repashy.com/ and
http://www.pangeareptile.com/forums/index.php. Both have very good care sheets available, as well as many experienced keepers and breeders for reference.
On the note of Anoles, I feel I should mention, they would NOT be a good option. They are very high maintenance. They need
UVB light, like beardies, as well as a good basking light. They are very high humidity. They only eat crickets. Most anoles in the pet trade are wild caught, and therefore have parasites. Unfortunately, 99% of people don't know or realize that anoles are so high maintenance, seeing only the very low price. Just another lesson of why research, research, research is so important before getting a pet, I guess, huh?