What type and rating of insulation should be used in a basement bathroom?
The best would be sprayed-in-place foam. Second would be foam board, cut to fit the space and then sealed in with spray can foam. EPS foam is fine, but if you are willing to pay for poly-iso you will get a better R value. I would go for a couple of inches thick of foam.

You could also do fiberglass, but you won't get the same level of insulation and you could get condensation in the wall.