Is that maximum price missing a zero?
Ford Focus SE with the Sport Package and no other options. It'll have Bluetooth--most nearly new cars will--but no MyFord Touch. A used 2013 will be far below $22,500. Even a new one will be well below $22,500 after discounts and incentives.
I'd like to suggest a base 2015 VW Golf, but even the S has a touchscreen. If you decide you can accept that, it's a great car.
A Hyundai Elantra GT doesn't handle as well as the Focus or Golf, but might still be to your liking. The 2014 and up have a reasonably strong engine. Steering weight is selectable via a button on the steering wheel.
What do you think of these? Maybe you want something larger, more powerful, etc.?