If the steering wheel is shaking at 50MPH, you can pretty much rule out that it is not because the wheels aren't road force balanced. This balancing technique becomes apparent at 78-85MPH, not at 50MPH.
If the tires have been replaced, and the problem still persists, I suggest you look into the wheels first to see if they are possibly bent.
If the wheels are in good condition, then we must begin to look at suspension hardware. You may have a bad ball joint, wheel bearing. It will not be your brakes, that will only cause vibration or judder when actually braking, not under normal cruising conditions.
After it has been diagnosed correctly, I strongly suggest an alignment. A poor alignment can really ruin a car from both perspectives: driving experience & mechanically.