Does this have a regular outlet plug and is there a minimum amount that you can put inside for it to effectively polish?

Yes, a regular 3 prong with the ground at 110v. In order for the tumbler to work properly is must be filled 3/4 - 2/3 full. If you underfill it, you won't get the proper tumbling action. If you don't have enough rock, consider getting non-abrasive ceramic media to take up space.