This is a tough one as there are so many choices and not much detail on your priorities so I'll focus on hot hatch versions that match your budget. Winter performance can almost always be dealt with with winter tires so I'm not going to focus is n AWD
1. Honda Civic SI. 2006-2011 had the high revving 2.0 ltr 2012 on has the 2.4ltr. If you can find a good one in budget look for the 2013.
2. Ford Fiesta ST may be in your price range for a 2014. Search for Bark M. Reviews on TTAC.com. This is one of the most balanced hot hatches one the market.
3. VW GTI 2013 -2015 look the most reliable but are above you price range 2011-2012 should be affordable.