I did 1x2 on the top, bottom, edges, joints, and at every stud. I ended up taking a 2x6 and ripping 3/4" strips cause it was cheaper and I had some extras. Since I was using white pegboard I painted the strips before the pegboard went up so you couldn't see the raw wood through the holes. I attached the board with white pan headed square drive screws.
Support it well, especially if you plan on hanging some weight on there. Using the correct hooks will help too.
When I first hung pegboard in my garage 10 years ago I didn't frame the perimeter and I had sections that would sag out because of it. I did the above on my makeover and wouldn't do it any other way now. Worked great.