Well, one of the best "starter" geckos that lives happily in a 10 gallon is a leopard gecko and that is usually what I suggest for a first gecko. IMHO they are very easy to care for and have great personalities. A leopard gecko manual is usually about $5 and a great resource to answer any questions you have.
If you where looking to just start a gecko in the 10 gallon, then only slightly more difficult to care for is the crested/ gargoyle /Rhacodactylus family. We raised ours in a 10 gallon until about 4 or 5 months when she received a cage extender making it approximately a 20 gallon tall. You can read through the sub-forum for this gecko as well as the leopard gecko.
Obviously, it depends on what you want and what you are willing to care for. A rhac or other sub tropical geckos will have similar environmental requirements as your other pet. A desert dweller like a leopard gecko needs higher temps, but you don't have to worry about humidity. I just suggested these two species since they are widely available, easy to care for, and come in amazing colors and morphs. But really, since geckos are everywhere but Antarctica, there are many to choose from!
Maybe if you offered us some information about what you are looking for? Fruit eater? Insects? Space? Temperature? Temperament? Handling? Then we can tell you some good fits. Good luck!
-----
0.1 Albino Leo Gecko
0.1 Crested Gecko
1.0 Dear Boyfriend
Departed: Harvey and Spock