I wouldn't put cories in anything as small as 6 gallons.
You can't keep male bettas with any other bettas, male or female. Certain females will fight, but you can try about 4 females. That whould spread the aggression out enough that one doesn't get picked on. It wouldn't leave you much room for other things, though, and there might still be aggression.
If you have a single betta, the sex doesn't really matter. All bettas have their own personality, and some will get along with other fish and some won't. You can usually do african dwarf frogs with them, or snails, or ottos, or common guppies (males may bite the tails of fancy guppies), or most other things you could put into a 6. I think females are a bit less aggressive than males if you want to put in brightly colored other fish.
You could also do a male/female pair of dwarf gouramis instead of a betta... or 1m/2f.