Schooling fish, you say? Neon tetras are, as DanDman18 said, a good choice. They're very small, so they'd be comfortable in a 10 gallon.

You mention danios, tetras, gourami, and platties.

1. Platties don't school, just so you know that. They are, however, very small and a good size match for your tank. Swordtails are too large for a 10 gallon.

2. Gourami don't school either. Also be careful because certain species of gourami grow too large for a 10 gallon tank. You'll be wanting a honey, sparkling, or croaking gourami. Any of those species would do. Check out aquabid.com's non-betta anabantoid section for more options: http://www.aquabid.com/cgi-bin/auction/ ... anabantoid
You'll be wanting to make a cut off, and exclude any species with a maximum length loner than 2 inches. Just type in the gourami name and 'maximum length' into google, and it should tell you how big they get. But again, gouramis are not schooling fish.

3. Tetras and danios. Now here are your schooling fish. Again, don't choose a species that gets larger than two inches. At one inch, neon tetras are a good choice. Zebra danios are two inches. You're really not going to be able to fit two schools of fish in a 10 gallon tank. Pick one species and stick 6-8 of them in there, and they'll be happy.

If it were me and I had a spare 10 gallon tank that I wanted to put a little flashy fish in, I'd go for Pseudomugil gertrudae. I've had my eye on them for a while; they're quite pretty.

Fish buying sources you might not have known about:
http://www.aquabid.com/
http://www.liveaquaria.com/
http://www.thatpetplace.com

My own personal list of 1 inch fish:
1. Apistogramma elizabethae (elizabeth dwarf cichlid)
2. Aspidoras pauciradiatus (false corydoras)
3. Barbus hulstaerti (african butterfly barb)
4. Barbus jae (jae barb)
5. Boraras maculatus (dwarf rasbora)
6. Boraras micros (no common name)
7. Boraras merah (phoenix rasbora)
8. Boraras urophthalmoides (sparrow rasbora)
9. Boraras brigittae (mosquito/chili rasbora)
10. Brachygobius doriae (bumblebee goby)
11. Carinotetraodon travancoricus (malabar dwarf pea puffer)
12. Celestichthys margaritatus (celestial pearl danio)
13. Corydoras habrosus (venezuelan pygmy cory)
14. Corydoras hastatus (black diamond cory)
15. Danio erythromicron (zebra rasbora)
16. Danio choprae (glowlight danio)
17. Dario dario (scarlet badis)
18. Elassoma genus
a. Elassoma gilberti (gulf coast pygmy sunfish)
b. Elassoma okefenokee (okefenokee pygmy sunfish)
c. Elassoma evergladei (everglades pygmy sunfish)
19. Epiplatys annulatus (clown killifish)
20. Etheostoma microperca (least darter)
21. Etheostoma tippecanoe (tippecanoe darter)
22. Hara jerdoni (asian stone catfish)
23. Heterandria formosa (dwarf livebearer)
24. Horadandia atukorali (platinum barb)
25. Hyphessobrycon amandae (ember tetra)
26. Leptolucania ommata (pygmy killifish)
27. Nannostomus espei (barred pencilfish)
28. Nannostomus marginatus (dwarf pencilfish)
29. Otocinclus cocama (zebra otocinclus)
30. Paracheirodon innesi (neon tetra)
31. Pseudomugil gertrudae (spotted blue-eye)
32. Rasbora dorsiocellatus (eyespot rabspora)
33. Tanichthys micagemma (sparkle-eye whitecloud)
34. Trichopsis pumila (sparkling gourami)

A one inch fish, like the ones listed above, would be happy in a 10 gallon tank. Not all of those fish are aquarium fish (some are way too rare), but it's the most comprehensive list I could come up with. Hopefully it gives you some ideas. If you type the fish's name into youtube, it should give you an idea of what the fish looks like and how it behaves in an aquarium (whether or not it schools).

Since you have your tank set up already, start growing some beneficial bacteria. Add fish flakes every day as if you were feeding fish. Buy a test kit for ammonia, nitrite, and nitrate. First the ammonia will rise. Then nitrite will begin to rise and ammonia will begin to fall. Then nitrate will begin to rise and nitrite will begin to fall. After about five weeks, it should be all nitrate, and zero ppm ammonia and nitrite.
More info:
http://www.fishkeeping.co.uk/articles_5 ... rticle.htm
Slide 8: http://www.ag.auburn.edu/~davisda/class ... Design.pdf

I'm a beginner with a 10 gallon too! I chose to start out with 3 GloFish danios, 2 tetras (cardinal and xray) and 1 fancy guppy. They're all very small, seem to do well with each other, and have PLENTY of space. 2 of my glowfish LOVE the guppy, they'll "school" together and swim around a lot... the other ones seem to mind their own business.

I would consider another fish or two, but I think with what I have and the clean up crew as well, I'm probably maximizing my space as it is.

I'll keep an eye on this thread, I'm curious too :)

Corys are much happier in schools, so if you are going to get a cory, plan on getting at least five.