If you are in an infantry squad, and your weapon gets destroyed, you'll take the weapon the squad leader tells you to take. Odd's are, that would be a Garand, unless the BAR gunner was killed and he wanted to keep the BAR in action.
If I did have a choice, I'd take the Garand anyway. It's more powerful than the carbine and the Thompson and is much, much, lighter than the BAR. Heck, it's even lighter than the Thompson.
You gotta remember also, that the BAR was actually somewhat unpopular. As soon as the BAR opened up, it got the attention of all the Germans in the area. I wouldn't want to be singled out for attention from a MG 42 by shooting off a BAR. Better to be just another rifelman.
My second choice would be the carbine. It'll still reach to 200 yards, which is far past the effective range on the Thompson. I'd only take it if no Garands were available though.
The enemy weapons would be right out. There's a reason they didn't let G.I.'s pick up and carry enemy weapons. As soon as you fire one, you're going to get shot at by both sides. The enemy will shoot at your because your shooting at them, your side will shoot at you because the sound of the weapon makes them think your an enemy. It's a no win. The only exception is if an enemy weapon is the ONLY weapon available.