I used 1x3 pine with 2" right angle brackets. I did not want to cover the walls with fabric so I built panels with 2" thick rigid fiberglass. I built my hangers out of 1x2" strips by ripping the boards in half at a 45 degree angle. One piece was mounted to the wall and one to the back of the panel frame. By doing this with a 3" wood frame I have two inches of spacing between the panel and wall. I am also in the process of lining the front wall behind the screen with the same material.
This one is of the bracket on the back. I just used a pnumatic stapler to attach the brackets to the back of the panel. Doing it this way, the panel was moved away from the wall about an inch. Again, I took a 1x2 and ripped it in half at a 45 degree angle. The bracket attached to the wall is about 12" shorter than the one attached to the panel so it can be slid along the wall for spacing between the panels.
The panel is 72X34 made from 1X3 pine. The rigid fiberglass is 2" thick.
I currently have three panels on each side with maybe two more added. There was no science in how I placed the panels but I do have the ability to slide them about 6" either way.