Sounds like you want a field gun instead of a trap gun, big difference. I've shot a little trap with bird guns, more with an 870 trap gun, recently an 11-87 trap gun. So far better scores with the 870. The 11-87 and I don't mesh, don't know why.
A trap gun is, to me, only good for trap but might be the ticket for pheasants, I've never hunted them. I think you can find a used O/U Citori for 1000.00, prolly not a trap gun tho.
I think wkuban hit the nail on the head. A dedicated trap gun is kind of a special animal. A good field gun can stand in as an informal trap gun but it doesn't always work well the other way around.
Trap guns are designed to shoot rising targets and are often single shot affairs unless you're shooting doubles.
Because trap generally requires only a single shell in the gun at a time, a repeater or double barrel isn't necessary. Other shotgun sports such as Skeet do require two shells in the gun. I've seen many trap rounds won with single shot guns or Remington 1100's loaded with a single shell at a time.
As for a good over & under for less than a $1000, that's not impossible but it may not be the best use of your money. I might lean towards a good field gun and maybe not even an over/under in that range. You might actually get more gun for your money if you don't go with an over/under type.
If you want a gas operated repeater, the older Beretta 390 series guns are hard to beat for reliability. A good used one can be found for under a $1000.
If an inertia operated gun is more to your liking, the Benelli is the way to go.
As for a new over & under, there are some on the market that might fit your price range but most of the new over & under guns that list for less than $1K are not ideal for field guns. You might be able to find an old Browning Citori for under $1K but be careful, those guns often have had a lot of use.
I'm very partial to Beretta when it comes to O/U shotguns but they are not cheap.
Take your time and think about what you really want to use the gun for. You may be happier with something that's not an O/U.
If you really want an O/U gun, consider saving your money up and getting the one you want to carry in the field forever.
Good Luck.