As mentioned, you should definitely stick to lighter target loads like #8 shot. Ask any clerk at a gun store and they may direct you to even softer rounds to start with.
Always hold the buttstock firmly in your shoulder - NOT your collarbone and not your biceps. Also, pay attention to your stance (keep your feet apart), bend your forward knee, and lean into the shot (i,e. lean forward). This will help you absorb recoil more efficiently and reduce trauma to your body. As said above: it should feel like you're being pushed, not punched. I have seen 120 lb girls totally unphased while shooting .12 gauge high-brass loads. It all comes down to technique.
If you want to be accurate with your shotgun then you should hold your dominant-side cheek onto the comb of the stock. This will naturally help keep your line of sight in line with the front bead (or front sight). Practice this and the muzzle will ultimately point exactly where your eyes do.
I am not sure what your intentions are with your new boomstick. But, considering this is your first firearm you should think about swapping out the coach gun for a longer barrelled sporting gun in whatever configuration you fancy. Then take lessons on proper handling and techniques for hunting, skeet, or defense. You may want to even downsize to a .20 gauge just so you don't beat yourself up too much while you're learning. Once you get confident in your abilities you will better understand your needs and can choose to get that coach gun or something more purpose-driven.
Don't be discouraged from side-by-sides and over-unders. They are classics for a reason.