Hrm, Neons could work but a lot of people here don't recommend them anything smaller than 15 gallons to be honest. Also Neon Tetras are active, depends on the Betta he might not like them being all active and he might get stressed out.
If you're into tetras try Ember Tetras, they're less active and smaller which is always a plus. 6 ~ 8 of them would be perfect.
Or if you use sand you could do Pygmy Cories, since these guys can't be housed in gravel since they're barbs will get damaged. Again 6 ~ 8 of these.
You can't really mix and match in a 10 gallon, it's quite hard and most of the time you'll probably end up overstocking. You can add in a snail and some shrimps along with the choice of your fish but that's pretty much it to be honest.