I have to second the Lefever DS suggestion as a gun to look at. They were made near the end of the Lefever production so materials are modern and most of the "improvements" to Lefevers are included. Almost all have steel barrels. Most have stocks that can be shot as is, not with the three plus inches drop of the early guns.
I found a high condition DS about three years ago for $750. I would not take twice that for the gun. I got lucky this year on a LC Smith for the same money but nine out of ten for that money will be money pits or worn out beaters. It is not the brand or the gun as much as knowing what are the normal problems and then knowing when a gun is a good value because it is correct and not some refinished, wornout piece of junk. You can find a high condition DS or a high condition NID for a grand. Much less likely to find any Parker, Smith or Fox in high condition for anywhere near that money.
NIDs are very decent guns, but some lament the styling of them. Few say that about them in small gauge, with a little engraving for some reason. Sterlingworths are solid gun and 12 can be bought in very nice condition for a grand if a later Savage made gun. Take the offer from others here and take one of them with you. Their education in what to buy and what to avoid will get you the best gun for the buck and save you thousands of buck in mistakes.
The best thing to do is to go to one of the larger gun shows where you can see a hundred double guns and look at as many of them as you can. When in doubt pass on any gun that does not look exactly like what you want. Do not settle for a gun.