Having been in that business, you're on the right track, it will greatlly improve everything from your grip to your ability to hold the weapon still, for longer periods of time, along with the benifit of a better shot because of the ability to aim without shaking your hand and body.
Basic strength building exercises, Bench press, plain flat press, is the fastest way to build upper body strength and add mass to your upper body. Along with lat pulldowns and lat extensions using cables or dumbells. Then a squat, also the core exercise to add strength to your core and legs, this will also help you stand for long periods of time without getting shakey. A bicep tricep superset is the final one I would give you to promote the arm and forarm. This all takes 5 minutes of circuit training with machines ,15 with free weights, 2 to 3 times per week or split it up to upper one day and legs the next. Cardio will top it off with half an hour 3 times a week, to build endurance and that burst of energy that is sometimes needed when you have to push through a door or shoot another round when you don't feel up to it. i trained too many professional athletes to brag about it here, but a simple quick 10-15 minute workout will work wonders for you, if you need specific help, email me and I will give you more specific stuff to do. We did this before here and it monopolised a lot of space, so I would prefer a private email or pm as to not interfere with the normal purpose of the forum, thanks., and don't forget to take in 60 grams of protein per day, it will put the muscle on fast.