1. When moving front wheels to back...do one at a time (left, then right). That way if it is a wheel you know which one. Check for loss of wheel weights, tire bulges, any thing abnormal.
2. Next cheapest thing is to check the front brakes.
3. Proceed to the struts.
If you end up going though the whole list and replacing the struts, also get an alignment. At that point you should be sitting good with no problems.
It is also a good idea while the car is jacked up to check all the front bushings for wear. The amount of miles you have there is going to be a bushing that needs TLC.