First, check the lug nuts for tightness. A lot of wobbles have been caused by loose wheels. Then have the tires balanced - a dynamic balance, not a static balance. If you don't have the time or opportunity to do that, you can swap the front tires for the rear tires. It may not stop the shaking, but if it is different or starts at a different speed, then the tires need to be balanced before you proceed.

Next, I would crawl under the front end and see if any of the steering parts are loose or worn. Have a buddy move the steering wheel back and forth (don't forget to unlock it), while you look for excess play at any point.

If you still haven't found anything bad or corrected anything, then take it in for a front end alignment. At that time, you can ask the front end mechanic to check the ball joints, etc.