Though opinions will vary, I tend to lean towards keeping it simple but effective. Best overall bet would be a 12 Gauge of course with a shorter barrel in the 18 to 22 inch range, with rifle sights and interchangeable chokes. This allows you to accurately use slugs, buckshot and is even fine for birdshot/small game as well. I prefer semi autos as i find them softer shooting than pumps. However pumps can reliably use lower power loads that may not cycle in a semi.
In your price range, the Mossberg 930 SPX or Remington 11-87 Deer would fit your price range in a semi. In the pump, Mossberg 500 or Rem 870 Deer would fit the bill.