My advice...
Do your best to figure out what you want and then be patient until you find a good deal on a solid gun.
I've found over the years that my preference is for old American made doubles, and more specifically for the Baker side by side shotguns. I love the sidelock design and how well made and solid the old Baker guns are. In my eyes they are as beautiful as they are functional. And for me it's as much about the history and the heritage as it is about the individual gun.
That kind of stuff may not matter to you though, or your likes may take a completely different path. But if you do have definite opinions on certain qualities that you want or feel you might enjoy in an old double, then pay special attention to that criteria as you look. If you don't then your purchase may end up being unsatisfying after it's all said and done.
Be patient and find a solid gun in safely shootable condition. Don't jump on something that's "almost solid" just because it's cheap... Trust me, it ain't a good deal!
That being said, I'll put my plug in for the Baker guns. Especially if your interests lean more toward the American vintage doubles.
For now the Baker guns have less collector interest than the Parkers, LC Smiths, Foxes, Lefevers, and Ithacas. So you can usually find a comparable Baker for considerably less than you'd pay for one of the others. Quality-wise they are every bit the equal of the others and in my experience they exceed the durability of a few. You should be able to find a very nice Baker made Batavia Special for considerably less than your price limit and may even be able to find a higher grade for $1000 or less.
Do LOTS of research, ask LOTS of questions, and handle as many guns as you can as you fine-tune your decision.