BALANCED, and well-built for that price range might be tough if you are talking about a gun that will also last.
A used AyA might be in your budget. The S&W Elite Gold that is currently discontinued and discounted would work - they are available ONLY in 20 gauge, but you can get English or POW grip, 26 or 28 inch barrel and single or double triggers...they WERE running around 1200, but now are creeping into the 1400 range. I own one and they are NOT as crappy as the Huglu guns from Turkey that CZ and others import. There were made by UTAS, originally sold for about 2400, and carry a lifetime and heirloom warranty from S&W for free repair. They have 3" chambers, chrome barrels, and come with fixed IC/M chokes