A little bit of play is acceptable, the coupler should be tight enough that the coupler won't come off the ball, but not so tight you can't close the latch. I typically tighten the coupler up until I feel a slight resistance when closing the coupler latch, then I'll back it off slightly from there.
Reese sells a white lithium grease that's conveniently packaged for use on hitch balls, part # 58117. view full answer...