It doesn't have a removable hood but the
North Face Venture is a great jacket and fits your budget. The pit zips are great since the jacket itself doesn't 'breath' well (it's a rain shell, after all). I've found that if you want a waterproof jacket that had good heat/sweat transfer you are going to be shelling out $200+ (more like $300+) for the really technical fabrics.
I've heard really good things about Mission Workshop rain shells, but they are going to be a bit more expensive.