I personally think it's easiest to just go with who you have right at the moment. ;P Committing to a party almost never works out for me - so when I want to run anything, I just see who of my friends is there, and ask them.
For a successful dungeon run, you ideally have a priest for healing, a warrior with defensive stance/growl/shattering strike for tanking, and one to three of any class, to deal damage.
There are some exceptions (east caves is fine with two, hollow tree doesn't really need a warrior, and even frigus can be doable without one), but as long as you have at least three people (warrior, priest, anything else), you can clear every dungeon in the game. The bosses' health and mechanics scale depending on how many you have, so you can clear them with three people as well as you could clear them with five.
