If your cash flow is good, I would do BCAA during the workout then muscle milk after the workout. I would recommend scivation Xtend. If your cash flow isn't so good at the moment, Protein over BCAAs any day. Also on a side note, Muscle milk is mostly a casien protien blend which is a slow releasing protein. Very good for a meal replacement or before bed, but after a hard workout you want a powder that is composed of mostly whey protein for faster digestion.
Welcome to AM btw