Welcome - you'll find a lot of experience here on the Tactical side / on the clay target or hunting side - I fall in the latter.
A 12ga is by far the most versatile shotgun gague / you can buy shells with 7/8oz in them so balistically it performs like a 20ga. A heavier gun means less recoil / as long as her upper body strength is sufficient to handle a 7 1/2 - 8 lb gun you will have a lot of options.
Personally, I'd recommend you start with something you can go to a Skeet, Trap or Sporting clays range with - and both of you, get used to the action types, the concept of shotgunning ( feel the lead, don't look at front sites, etc ) ... It will give you a lot of repetition with a shotgun / have some fun / really decide if she or you like the Tactical side of shotguns.
I'm a 1911 guy as well - and personally I rely on a Wilson Combat CQB 5" chambered in .45 acp for my primary carry and defensive weapon ...shotguns are a backup to me.
There are 3 "primary type" of action types in shotguns ( but OneOunce is correct, I did ignore Side by Sides, and single shots "...
In pump guns - lots of them out there - Remington 870 family, Benelli Nova, Browning BPS, etc . For an all around pump gun, I like a 28" barrel / good clays starter gun / will work for defense as well - maybe not the perfect "fighting weapon" - but being defensive, doesn't mean she or you need a "fighting weapon". A good all around gun for me is Browning BPS hunter model - 28" barrel - with screw in chokes retailing for around $ 500.
Semi-autos fall into 2 camps - gas operated Beretta, Remington, etc / and inertia operated ( Benelli, etc). Lots of pros and cons / I like the inertia gun - shoots cleaner. But lots of good entry level semi-autos out there like the Beretta 390/ 391's for under $ 1,000. Benelli makes a nice gun / some with comfort tech recoil supression system in them / Benelli super sport is a nice model but retails in $ 1800 range now. Lots of good used semi-autos out there too / if you know what you're looking at ( like Rem 1100's, etc ).
O/U's - break open guns. Most of the O/U's worth keeping long term ( shooting over 10,000 shells ) are the B guns ( Beretta and Browning ). Their entry level guns used are around $ 1,250 / new $ 1750. I would not recommend an O/U as a primary gun right away / although they are my primary hunting, sporting clays guns - and I'm a Browning guy, I like the Citori, XS Skeet model, 30" barrels in 12, 20, 28ga and .410 - but that's a $ 3,000 gun new.
Tactical shotguns / lots of them out there - Benelli M-4 is a nice gun / Rem 870 has kind of been the go-to tactical weapon for a long time / Mossberg is doing some decent things .... lot of options / you can hang all kinds of stuff off them / if you want. It isn't that I don't think they're effective / they are - but so is a good 1911 ...
If $ 500 is you budget limit - stay with the pump guns.
If you can go to $1,000 - look at semi-autos.
If you can go to $3,000 - look at some O/U's.
To me, each action type has its place / use. I use and like all 3 / but I use my O/U's a lot more than my semi-autos or pump guns. The key is practice / I shoot clays weekly / practice courses of fire with my 1911's weekly as well.