neon tetras play well with a lot of other species that arent large enough to think theyre food. I keep my neons with other tetras, danios, cory cats, tiger barbs, and guppies. mollies and rasboras would work well too.
Yep you could get cory's I'd say get at least 4 or 5 of them, if you really like them 6 wouldn't be out of the question. With 6 neons and 6 corys (assuming you pick a cory that stays in the 2 inch range or so) you could also fit a school of another type of fish...say pick a tetra or I personally really like harlequin rasboras if you have some green plants. You'd also have room for some ottos or a pleco that stays in the "small" range when your tank matures a bit.
Why dont you browse through the profiles? http://www.myfishtank.net/reviews/showcat.php/cat/2 or check out your local store and see what kinds are available to you before you make a decision? Mine are Julii cories I believe...they're great.
Check out what kinds of cories are available and appeal to you. For the most part, all cories act the same and most stay around the same size (2-3 inches). They'll shoal better if they're all the same kind than if you have one or two of a bunch of kinds.