I am installing a new Maytag, 2-stage, 3 ton AC. Plan on using 8-3 wiring for this. Will that be OK, or should I move to a 6?

I would use #6 and use appropriate breaker. Can only help your motor.

This depends on the length of the run you are going to use the No 8 wire on. And a three ton unit should work well on not more than a thirty amp breaker.