Can't go wrong with the flexibility of pegboard, make sure to get the 1/4" stuff, don't know if they even sell the 1/8" anymore. For the price of drywall, you can get 1/2" OSB which will take a beating compared to drywall and you can screw stuff to it without looking for studs. I have all three in my shop, even have OSB painted and unpainted. Either works fine. Pegboard on the bottom half wouldn't get my vote. Insulating the walls?
= Ole, not sure what you recommend - did insulate with batten covered insulation - so would you NOT put the pegboard all the way to the floor. This is a center wall and will house table saw, band saw and drill press. It is a half wall inside the garage between my shop and the one car parking side.