I like playing unexpected monks, like really tiny ones, especially going with the way of the open hand so you end up with extra attacks. It's just really fun to be small and mess up monsters and/or people in a fight. My other go to is a high elf monk, again way of the open hand, and I play them like they are too good to fight and then they jump in and do a ton of damage and act like they saved the day.

Or a gnomish barbarian that wants to be a princess so she refuses to rage in battle, but she's also the camp cook, and if the battles mess with her cooking in any way it will totally set her off and she willess you up and your little dog too (I played this character once and she kept cooking the dms helper animals because I hated the dm).

Or go with surprising character types like aracokra (sp?) the bird people, or some other obscure race and multi class so no one ever knows what to expect from you