You haven't really given me all the information I'd need to make a specific recommendation (budget? guage? action?). But here are some generally accepted principles of purchasing shotguns for clays.
"Buy a "B" Gun" - Browning, Beretta, Benelli, Blaser etc. Other guns are good too, don't get me wrong, but the "B" guns have a long history of lasting whilst shooting clays. 1 round of clay shooting is 25 shells. The B-guns are made to shoot thousands of shells without issue. Most hunting/field guns are not. I'm a rookie shooter and I typically shoot 75 clays when I go out. Do that weekly and it's not hard to shoot 1500 shells a season. Can you shoot clays with a cheap turkish gun? Yes you can, but I've also seen those fall apart with heavy use. B-guns are expensive, but they hold their value well and you'll often see them for sale in near-new condition because a lot of people buy into the sport and then decide it's not for them, or don't have time.
Buy a gun that fits. The most important thing about buying a shotgun is getting something that fits correctly, so that when shouldered and pointed at the clay, it hits where you're looking. There's tons of information out there about this that you can explore on youtube or google or whatever, but eventually you'll have to go into a shop with a large selection and shoulder some firearms and see what fits best. Hopefully you go somewhere with knowledgeable staff who will spend time helping you get setup. Adjustable stock guns are very nice, but also quite pricey.
Most people like break-action over-unders for clays, but I do see some semi-autos from time to time that people seem to like. I'd avoid a pump. I always forget to rack it between shots and it's a pain to load.
I'd suggest a 12 GA to start, you get used to the recoil and you can compensate with lighter loads or with the use of a limbsaver or a semi-auto. The reason for 12 GA is that it's more pellets, so you're more likely to hit the clays, of course, you'll still miss a lot. You can certainly shoot clays with a 20 GA and have a lot of success, but I'd suggest that it's a tad more difficult. I'm sure someone will say you'll be more successful with a better fitting gun with recoil you can handle, which is true, but if you can manage a 12 GA, it's advisable.
Your local gun club/clay range is a good source of information too. Your girlfriend might even be able to try out some of the other people's guns there before making a purchase. When I started shooting clays I was using a duck gun someone gave me, and having all sorts of problems with it, but I ended up trying a few at the club, and eventually buying my own over-under for use.
Good luck!