I know your looking for something a little longer in barrel for trap n stuff. But honestly I do have a cheap little SxS cai 20g coach gun that is just awesome and in the 8ish years I've owned it I've never had any problems with it. Honestly about one of the best gun purchases I've made and it was cheap! Always goes bang, light recoil, even pulling both barrels, and I only paid like $240 brand new. So sometimes some cheaper things will work out. But I am like most people for the most part and am willing to pay for a high quality part. I just happened to get lucky with that one. O and I've shot tons of rounds through it.
A Browning Citori would probably be your best bet. You should be able to find a good used one well within your budget. I have a 20 gauge that I bought years ago before Browning even put choke tubes in them. I had Briley install choke tubes and I shot registered skeet with it for a lot of years. It still looks like it is almost new. I also have a 12 gauge Citori that I used to win the Florida State Games gold medal in skeet, and it is still in like new condition. My point is that you just can't wear them out, so a used one makes a lot of sense not just because of the money you will save, but also because of the quality of the product.