Anywhere you want to run either component video, subwoofer audio, stereo audio, or digital audio (coax) you can pretty much do well with well-shielded RG6.
You may also want to look into undercutting that closet door and feeding a small AC vent into there.
When in doubt, run another cable to a potential subwoofer location.
Put a dedicated 20A circuit in the closet. Make sure they run the remaining power circuits such that lights and fans are separated from the outlets in the home.
When running audio, choose 4x14 gauge over 2x12 gauge and tie the pairs together. This gives you an extra pair of cables in the event one gets compromised somehow by a nail, etc.