Lemonsorbie, proper trap guns are specialized things. They are heavy and a poor choice for the field. Sporting clays and skeet guns are more suited to occasional field use. These guns are built for moderate to heavy use on target ranges and typically cost a little more than a field gun.
On the other hand, you can successfully shoot sporting clays, skeet and even trap with a field gun, and given your price range and desire to own an U/O I would recommend you consider a heavy field configuration.
Given your description thus far, you will most likely be happy with a gun which weighs 7 lbs. and probably a few ounces more. It should have 2 3/4 or 3 inch chambers, not 3 1/2 inches. The barrels should be at least 28 inches long. If your intended field use is primarily for waterfowl then look for 30 inch barrels. The long barrels will not hurt you in the field and they will help you at the range. From your description I think that interchangeable choke tubes are a must.
Within your price range you will be able to find a good used Beretta, Browning, Franchi or other similar quality manufacturers field gun which meets the above outlined specifications. These guns have receivers and lockup mechanisms that will withstand reasonably heavy use at the range. This is my primary recommendation, find a good, used mid grade field or "sporting" gun from a major manufacturer.
There are new guns available in your price range. One interesting prospect is the Savage Milano, an Italian made gun (I. Rizzini) with sufficient heft for your purposes, at a relatively low price. It is of unproven quality (to me), but it should be worth a look.
In my opinion (and for a variety of reasons) the Turkish and Brazilian made guns are not well suited to intensive target shooting. Of the inexpensive U/O's I think that the Baikal is as tough as old nails and can probably be used for anything. However, the Baikal does not handle as well as the Berettas et al. That is why I recommend that you go the used, mid grade route.
Gun fit: For you, a stock with at least a 14 1/2 inch LOP will be required, likely 14 3/4 inches. Drop, cast and pitch measurements are up to you, but the goal is to find a stock that lets the gun shoot where you look, rather than you having to adapt to the gun. Try as many guns as is possible. Seek assistance wherever you can find it. Good gun fit is important, both on the range and in the field.
Buying a shotgun is supposed to be fun. Trust your instincts and ask lots of questions. Take your time and enjoy the search. I wish you well.
Sharptail