I've had that happen, too. Most of the time, they wouldn't even notice each other, but, once in a while the betta would swim down to flare to prove who's boss.
The corys would usually just roll their eyes and swim away. :laugh:
That's so funny!
root81: I just realized that no one has answered your second question of which to add first. Adding the other fish first and the betta last would be the best idea. If the betta has the tank to himself for sometime before other inhabitants arrive, it's likely he'll be more aggressive and territorial to the newcomers. If he's added last, however, he may realize that he has to share the space with the fish who were there before him.
Of course it depends on the personality of the betta you choose. Hope it's a good one!