Dedicated circuit

+1 for jea48 and gs5556

Unfortunately, the ac compressor is going to infect the whole house, it won’t be confined to the subpanel. Running a 100 foot branch circuit makes it a magnet for EMI generated throughout the house, so I would use 3-wire romex. The wire is pre-twisted and helps with rejecting common mode noise, which could be a problem at that distance.

So, I assume using 3 wire I would combine the two hots, giving me an effective gauge increase.
At this point I am only installing one outlet for my amp.

 The 3 wires would be hot (black), neutral (white) and ground. I would at least have a double outlet box, 4 sockets pig tailed.

I plan on running 2 outlet boxes to my room. One outlet box for my amp with 2 sockets on the front wall. And then a 4 socket outlet box for my components on the side wall. I don't need 4 sockets right now, but in the future I may. It is easier to put in extra now than have to add outlets later. I am going to use some PS Audio outlets I have lying around to start. So the dedicated outlets in the room will be light grey, while the rest of the outlets in the room are white.

To me 3 wire is,for example, 12/3 w/ground.
so I could run 12/3w/ground tie the hots together and end up with an effective gauge of 9