QB? Squat and dead lifts for sure, throwing a ball is a full body motion and those are the barbell lifts that involve the more muscles anyway.

Bench press, military press and bent over rows are the norm for upper body. I would add some biceps curls, abs works and off course cardio to that.

In your situation, what is even more important is the rep/set scheme tho... You need strength over size has a QB so I suggest 5 reps 5 sets... Sometimes switching to 4*6 or 3*8 might be a good idea tho.