Hi Len Henry hits the nail on the head. I'd follow his advice verbatim.....
After you scrub with TSP (I'd use it straight...but be sure to wear rubber gloves and some kind of a mask), sand using a random orbital sander (ROS) and non-clogging disks (they are attached to the sander by hook&loop (velcro). As Henry said, don't try to sand the paint all off (although the ROS will do this if you aren't careful), but rough the surface well. Remember....sanding is not cleaning. If you don't have a ROS, buy one. You'll use it for many years. Porter Cable and DeWalt make good ones.