I would third ninja. It has good combos and I believe in the current meta is it desired. The ninjitsu combinations can take a little getting used to, but eventually it comes naturally. It also has some support skills. The ninja aesthetic is really strong though (always crouched down, "Naruto" running, the jump is a forward flip), so I don't know if that would be a turn-off for you like it was for me.

Monk is also a very good contender. The combos are a little more complicated, but it's very active with its positionals and just generally fun to play. It's known for its raw power, and currently it has some of the top dps numbers in Omega Savage (Although it is mostly drowned out by tons of Samurai). It does take a bit more effort to get to that point though, compared to the likes of samurai or red mage.

Bard is active and is definitely a support!DPS, but it doesn't require nearly as much moving around as the other two do. But definitely give it a shot, it might just be what you're looking for!