Trying to get that room to sound good will make you go crazy. Sound is going to be 'meh' at best - the 13' dimension is too small and those sloped ceilings will create a nightmare. If you want to have better than average sound, keep looking. Or build one.
Would this room work?
My wife is falling in love with a house that has a room over the garage 13 feet by 17 feet, ceiling height 8 feet at peak with sloped side walls to 4 foot wide peak which runs lengthwise. This room could be a dedicated listening room with any room treatments I desired. Does anyone have such a room and does it work well? Issues and challenges?