I'd add one caveat to Rocketman's post. About the only English gun I can think of that doesn't fit his model very well is the BSA, which is a machine-made gun, as opposed to virtually all the other Birmingham boxlocks, on which most of the work was done by hand. If you pay the same money for a BSA as you would for another Birmingham nonejector, you've just made a costly mistake. And I'd also add that you're talking strictly 12's if you're interested in keeping the cost down. There's a significant premium for the smaller gauges.
Jake, in your suggested price range, the Scott 700 is a good place to start. Modern gun, and as Rocketman said, pretty much bulletproof. But there are quite a few BLE options in that $2500-3000 range.