Congratulations, you’re on exactly the right track when leaning toward a 20ga Remington 1100. It’s a soft-shooting smaller frame that women can handle more easily than any 12ga. You can find a good one for not a lot of money and, speaking from a lifetime of competition experience (mostly Skeet, but quite a bit of Sporting also), they will shoot all day, every day, with very little maintenance. Take care of the gun and if-and-when your student wants something else, you can always get your money back out of it. I personally shoot mostly over/unders but have lots of friends/family/acquaintances who shoot 1100's and 11-87's. I am presently coaching an adult woman, about 5' 2" and barely 100lbs, who had no prior experience and who is doing extremely well at Sporting with a 20ga 1100. The Winchester 1400, by the way, would be a very poor choice.
You’re getting a lot of advice, some good, and some wrong-headed & misguided. If I may elaborate;
1) Browning Gold’s are known widely among heavy competition shooters as jam-o-matics. Browning shooters are loyal (I personally carry only vintage Browning A-5's and Superposed’s when hunting) and will argue, but facts are facts.
2) A 12ga is a poor choice for a woman beginner. Within competition circles, large grown men shoot guns in the 9lb to 10lb range (some even heavier) to reduce felt recoil. In Skeet over the past decades many champions in the 12ga event were shooting 20ga guns/tubes. I personally have won major 12ga events shooting 20ga tubes. If you want your student to enjoy and continue the game, protect her from recoil as much as possible.
3) I love over-unders, but recoil is greater than with a gas operated semi-auto. See point 2) above.
4) Remington makes good youth/women’s stocks, and any name-brand recoil pad would be about as good as any other. A too-soft pad will wear out too quickly.
5) The only reason a 12ga pattern is ‘better’ than a 20ga pattern is that there is more shot in it. See point 2) about Skeet World Champions who shoot the 20ga in 12ga events. In Sporting circles most men shoot 12's because target distances are longer.
6) Trap shooting and trap shooters have almost nothing in common with your situation. They all shoot 12 ga guns with lengthy barrels, tight chokes, and stocks & ribs that are useless in any other shooting discipline.
7) From personal experience with four guns among friends and acquaintances, any Stoeger would be a terrible choice for reasons too numerous to list here.
8) Your wife, a beginner you would presumably like to see remain enthused and eager about shooting, would at this point NOT be better off with any 12ga, any over/under, or any pump.
Good luck, and good shooting
