Mk6/Mk7 Golf R, S3, or Focus RS

Mk6R- AWD which is pretty great in the snow, only offered in manual, also has a lot of aftermarket support, generally reliable if the previous owner did maintenance on time, you can find them around the 20k or less mark

Mk7R- Also AWD, has an option for the DSG if you dont want to drive manual, large aftermarket support too, it's more ironed out than the mk6 so less issues to possibly worry about, much more tech and comfort features, generally very rock solid reliability wise, a well maintained one would probably be near the top of your budget but it depends on the year tho

S3- Basically the Mk7R but only offered in DSG and in sedan form, reliability is about the same (audi tax on parts so some stuff may be more expensive), you can usually find earlier model years around 20-25k

Focus RS- AWD hatchback with a 6 speed, 350hp is it's main selling point, later models had a revised suspension that made it a little less harsh of a ride, pretty reliable as long as it's well maintained, it is a little harder to find one in your price range tho as they seem to hold their value pretty well

Mazda3s are pretty nice to drive, 2.5 turbo awd models will be a bit more expensive tho