If you are looking for a specific brand, have a good time. I would shoot every gun you can get your hands on and figure out what works best for you. Forget the cost of the gun, well as much as you can as if you get a $500 gun and can't shoot it worth a darn you have a $500 paper weight you now need to get rid of. I am sure you will get people saying buy this gun or that gun and they are all good advise with the idea of try the gun and see if it works for you. I have shot alot of different guns trying to find something that worked and didn't really care what it costs and ended up with a Super Sport as it just worked best for me. That being said the gun is by no means a trap gun and for me performs the wost at trap. I probably like trap the least out of the shooting I do and the gun works for sporting clays and dare I say Skeet the best for me. Again that is just what works for me. Go to a club and I am sure more people than you think will shove a gun in your hand and say try this. Also keep in mind if the gun doesn't feel correct to you, it's not insulting to say the gun doesn't feel correct. That is the reason there are so many different guns out there as no one guns works for everyone. If it did this would be so much easier for everyone.
Take a good look at a good used Remington M1100 in field grade. You may have to put a couple of pieces of mole skin on the comb to raise it up to a decent height, but it may shoot OK as is. I've only run into one M1100 stock that would cause me problems with 16 yard targets - even field grade stocks. Put on a good recoil pad, put a pin in the barrel to knock down the hulls and you should have something that works OK for under $500. For $700 you can probably find a good used trap grade 1100. A couple of days ago I was in Gander Mountain and they had some new plastic stocked 11-87's for $500.
These are not guns you will wind up with for overall trapshooting but they will do OK for 16 yard singles and early doubles. As you grow into the sport, your tastes will change, you will shoot your buddy's guns, etc. Then you can save up for what you may really want or need. There are a lot of people that use 1100's and Beretta 390/391's as their main gun and are very competitive. However, they are usually tricked out and will bust your $700 budget.