I'm wondering why nobody suggested putting light pressure on the brake pedal when you notice the shake - if it gets worse, you have a warped rotor. If it doesn't, then at least you know the discs are fine... :thumbsup:
Also given that it's a car from a private sale, there's nothing to say the previous owner didn't mount a kerb or disappear into a pothole - as suggested, one rim might have a slight bend or warp - that might also go to explain why they have trouble getting the wheels to balance!
Just a coupla thorts for ya...
Cheerz!