6 neons and 3 otos would be fine, but you can't put anything else in a 10 gal.
Both types of fish are rather sensitive, so you must make sure your tank is completely cycled and stable before adding the neons. Then I would wait a bit to put the otos, so they'll have some algae to eat.
Both types like some plants to hide in and otos appreciate a piece of driftwood.
You could put fish from two of the groups you've chosen, but not all three. Since they're all pretty small, they shouldn't add up to more than around 10" total length when adult size.
And no neons with bettas!