I'm not sure why someone would think neons do not swim much. They are extremely active fish and again are not the best idea for a 10 gallon. If you put a school in a ten on their own it is over stocked, adding platy on top is just overload. I know everyone seems to think that neons are these little fish and there for they must be great for little places but they aren't.
I have a school in my 20 gallon and next to my harliquin rasbora(another poor fish being stuck into tiny spots) they are the most active fish in the tank. They use the whole thing, top middle and bottom.
Platy are also messy messy fish. Mine are little poop factories. 3 at most in a 10 gallon will fully stock it. 10 gallons really isn't that big you need to realize. Most fish are not suitable for this size tank. The smaller you go the more water quality issues you will have as well and it's added stress on your fish they just don't need. If you are really stuck on neons then you really need a bigger tank to be fair to them and their needs.
Platy are not schooling fish but they are social and like to have company of their own kind. 3 is a good number to start with.
If you really want schooling fish you should look into the nano fish that have been mentioned they are the most ideal fish for this tank set up. You can happily keep a school of 6 or 7 ember tetras, chili rasbora or celestial pearl danios.