Recoil in a 12 ga. is going to be worse than in a semi-auto. I shot competitive trap and skeet for more than 10 years. A 12 ga. O/U is by far the prefered shotgun of competition shooters. I recommend you find an old Winchester 101 and have Briley add choke tubes to it.
The Winchester 101 has the unique feature. It has mechanical triggers. This means if the first trigger pull fails to go off, you can simply pull the trigger again to fire the other barrel. Most current O/U shotguns have an inertia trigger. This trigger requires the recoil of the first round going off to reset the trigger for the second round. First round is a dud, you have no second round unless you bounce the butt to reset the trigger. Not a great idea by the way.
If recoil is a problem, you can always add some kind or recoil reducer into the butt stock. My Beretta has 12 ounces of liquid mercury in the buttstock. It is in a sealed PVC tube that slips into the bolt hole in the buttstock. A quick five minute improvement.
This additional weight on your shoulder helps with swinging the shotgun to the target.
You can get by in Skeet and Sporting Clays with a typical "field" shotgun. Trap shooters use a more specialized shotgun with a much taller ribbed sight since trap "birds" are going away from you, and also rising as they leave the area. Shop around, there are plenty of used shotguns out there.
When are we going to do it?