Will your partner be shooting along side of you at the same time ( if so, now you're needing 2 guns..lol )
or just every now and then taking turns, with your guidance ?
To share a gun, and to be easier on her small frame I'd suggest a reputable semi-auto with a few different chokes.
Both 12 ga and 20 ga are very viable options for either discipline. I shoot with a lot of folks who have gone to solely 20 ga for all their shooting needs...just for the recoil factor alone, plus, they're smaller, lighter guns, even better for smaller framed people.
IMHO...buy the best you can afford ! Go with a reputable name gun. Gonna cost you more, but if you buy once you cry once.
Some good shape used ones around in a few places...you just need to look every day, cuz the great deals are gobbled up quickly.
These guns hold their value pretty good to, so if life changes and you decide to sell out, you won't loose much. You never mentioned caliber, so I'm assuming12 ga. Single barrel semi auto gun will be lighter and easier to swing for you and her.
Beretta A400 with the recoil reduction is a very popular one with a lot of men AND women, also has a legend of problem free shooting reputation !! Several of my squad mates shoot them...from the blue "smurfette" model to the newest ones!
Biggest drawback with semi's is picking up your empties..lol The new MOJO "Pic-up Stick" will save your back a ton !! Winchester SX3 Sporting is another good semi auto made for Sport shooting, I have one, also have a Browning Maxus Stalker that my SIL uses solely for sporting clays and skeet ! Never an issue in 4 years of shooting lots of targets !! Keep them clean and they run like new ! I usually shoot my Browning 625 O\U and my new Fabarm N2...also great guns.
There's LOTS to choose from in semi's and O'U's....but buying a shotgun made for sporting shoots is your best bet. The others just won't hold up to any amount of shooting. Ultimately, your wallet is gonna decide WHAT you'll be buying...talk to it
** OP...few things to consider.
To shoot 2 different disciplines..ie..skeet and trap you will need different chokes for each one. Easily changed out with a semi or O/U . Semi-auto....You can get by with 1 full and 1 skeet. Now with an O/U...you'll need 2 of each.
Trap can be shot as all singles...or it can be doubles also. Your club will dictate that. If you're gonna be shooting both , you'll need a gun that will hold two shells and should have full choke capability. This is where changeable chokes is advantageous.
The game of skeet always has doubles, and is shot with more open chokes...ie..skeet, improved cylinder. Again, changeable chokes has it's advantages.
Keep an eye out on the EE here...the gun dealer also always has a bunch of used sporting guns...give his site a look every day or two. His inventory changes sometimes in hours.
Hope you and her continue on with your skeet / trap, and who knows, maybe some...sporting clays shooting in the future (it's the most fun you can have with your clothes on !!)
Best of luck with it...the fun is only beginning for you guys ! Keep us in the loop...I'd like to know how you made out and what you decided.
Cheers...Kevin