A hang power clean is cleaned from somewhere between the floor and the high-hang position, you can pull from above the knee, below the knee or mid thigh. I'd say above the knee is most common. And you catch the weight in the "power" position.
Hang Power Clean:
A power clean is from pulled form the floor and caught in the "power position":
A clean is from the ground and caught as close to or in the front squat position. You can do hang variations of the clean.
I guess my question is what do you want to get out of adding the clean? I'd start with the power clean if you are looking to just add and explosive movement into your weekly workout. If you are looking to get more into Oly I'd recommend some coaching as not to get any bad habits early on.