The floating feeling will most likely be from the suspension. My guess is the shocks. The vibration can be a few different things. The most common are warped brake rotors, it will vibrate when braking as well, and unbalanced wheels. Suspension wise if you're not planning on keeping the car bone stock then I highly suggest looking at upgrading the whole suspension. You don't need to purchase a high end 4 link, they are awesome though, to get a drastic change. Even upgrading the springs and shocks will make the car a more enjoyable ride.
If he is not braking during the vibration, its not brake rotors, its most likely ball bearings in the control arms. Unbalanced tires very likely. I just got new tires and didn't get them professionally balanced yet. Anything over 55mph starts shaking.