I inherited a team of moderators. Within three months, the admin and three of her friend moderators were well on the way to burning a hole in my stomach lining. I wasn't innocent in this - some mistakes and some arrogance on my part, I'm afraid. They were certainly not innocent either - didn't like the fact that someone else had taken over who didn't like the hardassed 'slap them all with infraction' style.
If you've got drama queens, though, do what I had to do. Drop them to member status and say "Thanks, but no thanks." You have the good of the community to look after. You can try giving warnings, but they will only last so long. People revert to type. Some people relish the power. If you have two constantly infighting mods, drop them both.
Moderator selection on my main board is fairly democratic. If I reckon we need a new mod or two due to activity levels, I discuss it with the team. At that point, I ask for suggestions, though I usually have ideas in mind. We base this on peoples' activities on the board - how they deal with newbies, how they deal with arguments (do they debate or skirt the belittling line), are they well-liked, and most of all have they got a sense of humour. When we have a name or three we all agree on, we delete the discussion thread in the mod section and then I make some invites in private. That's the only question I ask of them.
Another forum I run is one I started from scratch. I've only ever needed one other moderator on there. He was active and has managed to keep things under control quite nicely. That said, considering the lack of rules on there and the general respect of the members for each other, it's a fairly easy task. One banning and one thread closure in nearly a decade can't be bad
In your situation, if you're going to start a forum from scratch, I'd do the work myself for a while and see from the gained members who you want to offer the position to.
Rapscallion