I would get at least 20 gallons if you want to breed feeders. Easier on the maintinance. You could use the 10 to grow out a few fry in though from a different tank.
Platies are a good choice, you can keep them in lower temperatures. Since you want to avoid a heater, if your room temperature is around 75 I say go for guppies and convicts, They should be ok at that temp. Last year before I moved my dad forgot to put the heater back in on my guppy tank and they were thriving in the mid 60's, no idea how! Remember it takes them a while to grow though so they will be a treat only ever so often. A barebones 40 breeder with a bunch of livebearers would be a cool tank though, you could enjoy the community aspect while having a good way to dispose of all the babies. Haha.