Chase, I don't know enough about the guns to recommend anything, but should you get an SX3, there are a few models to choose from. Since you say you may want to use it to hunt, note that the SX3 comes in a few models.
If you want it for skeet and trap there is a sporting adjustable model. It has a 2-3/4" chamber, which may not be what you need for some prey. It is more expensive, but you may find one for not much more than $1000 new. You should be able to find a used one withing your budget.
Even if you don't go with the sporting model, you probably will want a 28" or 30" barrel.
BigJimP may be along soon and he has much more experience with trap and skeet, plus one of his faves is a Benelli SuperSport. The Stoeger is similar to the Benelli and is an inertia gun, whereas the Winchester SX3 is gas operated. Trap and Skeet shooters are often looking for softer shooting guns since felt recoil is more of a problem to them due to the fact that they shoot a lot more rounds in a short period of time than do hunters.
In general it is a very good idea to shoot a gun before buying, even if you have to rent one if available in your area.
Last edited by TheKlawMan; November 25, 2012 at 03:37 AM.