Front end shake on 2001 Ford Taurus

My son just purchased his first car. Car runs and handled fine for the test drive, but was unable to take it out on the freeway. Anyway, now that we've had a chance to take it out and get the speed up, it has a bad shake starting at around 55-60 mph. It appears to be coming from the front end somewhere and it transmits through the steering column really bad. Not really noticeable below that and no noise issues when turning the wheel left or right at city speeds. Any ideas on what to check and how? Thanks for your time.

First thing to do is have the tires balanced, Usually if the shaking is at a certain speed it means one or more of the tires are out of balance