Steering wheel shakes

You may have more then one problem. The fact you say the wheel shakes when you apply the brakes leads me to believe the rotors are wrapped and need to be replaced. After replacing them see if the shake goes away. I suspect this will correct the problem. However if it doesn't the next thing to do is to have the wheels balanced. If you still have the problem then you will need the have the front end inspected.
Backyardmechanic 8)