Please read the thread "what have you shot at home accidently". If you want to save your garage, garage door, car, goat.............. make it a good one.
3/4" plywood or something good like 3/4" particle board if you don't want a hole in your garage when you miss your bag target. I don't know how you do that in a typical garage, but it looks like it happens quite a bit. I usually only miss the bag when things go wrong on a shot when I get past 20 yd. and my garage is not that big. I would put a section of carpet in front of that to save the arrows from damage. I would put the fibber side facing you. I think the fiber side will pack more and prevent penetration better than the backing. Kind of like cutting from the back side of a hide. It needs to be out a couple feet from the plywood or wall so it can move to absorb the shot energy. The plywood is the last resort to make sure you don't shoot out the garage wall.
Last year at the Kalamazoo expo they used heavy cloth tarps of some kind as a backer hung from a line. The shooting was fairly close in distance. I want to say it was about 10 yd. It stopped field points no problem without penetration. You have to have it out a few feet from a wall so it can absorb the shot, but that worked great and would be all you need.