Based on what ScottWax uses for polishes with the UDM it appears that Optimum line works great. I would also give
Menzerna line a shot. If you're doing some paint correction you'd want at least 106ff and possibly IP as well. I'm running 106ff and HTEC for mostly all the work that I need to do. I generally use the rotary for both of those application, and haven't tried it out with the UDM yet.
Also pick up some LC CCS pads, white & orange ones should probably be all you need for any paint correction.