Steering wheel/front vibrate when braking at highway speed

Sounds like your front drums could be out of round - the inside surface of the drum is not a perfect circle so the brakes kind of stutter and shake the front end. Drums would need to be turned or replaced.

How long have those wheels been on the car? Are they recent?

Is there a way to check if the drums are not round? The wheels have been on for some years now. The past few years I have worked more on the car than it has been driven, so I honestly can't say how long this vibration has been going on. But now I would like to drive it as much as possible.