If you don't like playing classes with a rotation that's set in stone, I'd recommend machinist. They're a range dps class that works primarily from prioritizing certain skills above others. Their rotation changes a lot, mainly due to the nature of their main damage abilities being RNG based. It does require a lot of focus, as you have similar supportive capabilities to that of a Bard and your burst requires a lot of preparation as well as thinking a head constantly. It's very rewarding to play.

In all honesty, it's not a bad idea to try out all of the dps classes to get a feel for them and see which one you'd enjoy playing the most. Wouldn't recommend monk though. Or dragoon.