SL, welcome. I've been looking at your diagram and pictures trying to figure out a good placement in those tight quarters. The present arrangement is possible, but my thought would be to put the head of the bed where the 4' dresser is and the dresser about where the TV is. Then set up TV and 3 front speakers along the wall with the window. Mount QSs about 6' up on the back wall to the left and right of the bed(work around the door as best as possible).
As far as speakers, I have M22s and they would be excellent in that size of room although you could even go with M2s if that would fit your budget better. You don't need QS8s in that size room; QS4s would be plenty. For a center the VP100 is fine, but my own preference would be to use a vertical M2 center. You can consider a smaller sub, and one that's possibly more cost-effective than the smallest Axiom sub would be the Hsu STF-1.
For speaker wire regular 16ga lampcord for 20 cents a foot or so is all that's needed for those short runs.
Yes, you'd need amplification, and there're many fine receivers available, depending on your budget. In the $400 area good choices are offered by Denon, HK, Pioneer and Yamaha, among others.
