So I suppose you already know about cycling and will do a fishless cycle first? (read through the first three links in my signature)
I think guppies and platies are a good place to start if you aren't too experienced and want something attractive and interesting but also hardy. I think platies, in particular, would work great. The only problem with livebearers is their tendency to over-stock a tank by producing fry non-stop and of course you need to keep them in a ratio of at least 2 females to every male. If you aren't interested in dealing with fry, get males only (easily distinguished by the rod-like anal fin or 'gonopodium' when compared to the female's fan-shaped anal fin).
Other fish you could include and are quite hardy are honey gouramies (a male and 2-3 females would work great), white cloud mountain minnows (though I'd preffer a larger tank for these myself and they like to be in a group), bronze or peppered corydoras catfish (in a group of 4 at least) , black phantom tetras, harlequin rasboras or checker barbs - all of which should be in a small shoal, a couple of cherry barbs, other small rasboras, tetras or barbs and some of the smaller species of danio (not zebra/leopard, pearl etc though - these more common species usualy require at least a 20 gallon tank because they are very active) and you could also try an american-flag fish.
Then there's shell-dwelling cichlids, killifish, certain small gouramies and dwarf puffers which would all work but might be more difficult or require extra research.
There's a lot of choice out there - and don't over-look the number of invertabrates like shrimp and snails that would love a 10 gallon and there' will always be african dwarf frogs and similar oddities