10x13 is doable for a small HT room. Congrats!
Honestly, it you want to do it right -- tear out the drywall/floor down to studs. It will let you run all of your cables/wires and somewhat improve the sound isolation. Unless you are willing to uncouple the room for sound isolation, then I would simply suggest good insulation, double drywall with green glue, and seal everything up tight. That would be my minimum -- and you would lose the least amount of space.
Any chance of having the equipment in a closet/out of the room?
Room/Sound treatments are every bit as important as the equipment you buy. Good room treatment can make cheap speakers sound good; no/poor room treatment can make $20k speakers sound poor. Usually it is a relatively cheap but labor intensive aspect of our HTs!
Good Luck and welcome to our crazy club!