Brick is by far the most common in the UK. Usually brick outer wall with an insulation gap and an aerated concrete block on the inner wall. Sometimes two concrete blocks if it's to be rendered (stucco?).

Oak wooden frame is sometimes (can be expensive) used but the wooden cladding approach is very rare. That said prefab panels which combine stud work insulation etc are sometimes used. Not particularly commonly but they are quite new. I'd have made pre-fab panels for my workshop but I ended up using brick as the fire rating made building control regulations easier to pass. It took me a long time to lay all the bricks though so I may have made the wrong decision!