You need to raise the classes job levels to get them to do their proper damage and yes Monks are significantly better empty handed. It shouldn't take too many job levels to see an improvement but their equipment pool is pretty limited so they do come across as glass cannons for certain sections of the game. Another reason to bother with Monk Job is due to their high Vitality stat. It is the only stat that affects your character on level up, raising your HP, so if your characters have HP, level them up as a Monk (or their upgraded class) to net them better HP.

Unless your party combo isn't cutting it right now, I feel you should be fine with the group you have to be honest. I wouldn't really experiment with different classes until you have the airship back and have easy access to towns. I usually return to Ur and fight Goblins to raise Job levels quickly, you don't need high levels either so it's not as much of a grind as you think. The fastest way to level a job is to make use of their special skills in battle.