Not sure if you are wanting long range precision or not but I believe the M1A1 has a shorter barrel that may affect your long range accuracy. The barrel will be something you may want to change as well to squeeze as much as you can out of her. Stocks are a personal preference and what fits you the best. You can dump a lot of money into the conditioning of a M1A. McMillan or JAE stocks, Kreiger or Douglas match barrels, spendy European optics, etc.
What's your budget?