I'm sure the thief will get most invites because they have other functions than being just a damage dealer. THF's real only purpose as a damage dealer is to SATA weapon skills, other than that their damage out-put is rather sub-par.

It all really depends on what a party needs. My understanding is that DRGs have the hardest time getting parties. SAMs don't really come into their own until level 30 when they can do two skillchains at a time. DRK are always good for damage dealing. They hit hard and if you're a hume, mithra, or tarutaru they can magic burst decently if they keep elemental magic up and drain can do some serious damage. You should already have a good idea how MNK works. WARs are also really good because they can tank well while dealing big damage to keep hate.

I can't really tell you which is going to do the most damage, it's all situational. Goes with whatever seems to suit your style.