Definitely abstract algebra and real analysis. If you're doing stats, make sure it's calc based stats.
I would probably look more into other proof based courses like a basic proof course or a number theory course. The more experience you have, the better off you'll be.
Maybe try for a PDE course or complex analysis.
I guess as far as master's vs PhD, if you don't feel confident enough for a PhD at this time try for a master's and take that time to get your feel for graduate level work and what areas really interest you.