Overall I'm a fan of co-op, but practically I've spent very little time on PvP.
I think hunt is the best if you're playing with people you're familiar with and who can operate as a team. Checkpoint is alright for when there are lots of randoms joining. In short, I'd rather play hunt if it was GC members on and checkpoint if it was randoms on.
I wouldn't be opposed to multiple servers if you think we can get the draw. However, we need to figure out how to effectively and efficiently run an Insurgency server given that it's apparently some horrid amalgamation of something from CS:GO, Portal 2, and something someone who knows more about computers can explain to me. When we figure out our first server, I'm down if you think it's viable to have multiple servers. For now, I think the co-op game type is probably the easiest to run as an admin during a stage where we're still getting a feel for people's interest in the game.