If no one has mentioned it, remember to tuck your right elbow in tight against your body, and support the weight of the weapon with your right hand. The only thing your left hand does is steer, take as little weight with it as possible. This is tougher to do with the longer barreled guns. You want the toe of the buttstock to be pivoting up into your armpit. This also helps counter climb on the FA Tommys. Keep your head back, only lightly touching the buttstock. Both eyes open if you can manage it.
Believe it or not, I got to qualify on the Thompson in the USN in the early 1990s. Some ship armorys still had them.