Could be so many things.
Try getting up to speed where the shaking is easily noticable and shift into neutral. If it goes away then it could actually be driveline related

If it continues, even in neutral, it's probably wheel/tire/brake related.
If you can feel the shaking through the steering wheel its almost always out of balance or out of round front tires. If the wheel pulls to one side or another in unison with the shaking it could be your front brakes dragging. If it's more of a pulsing sensation while braking to a stop it could be warped rotors or improperly torqued lug nuts.
I've seen all these things cause some of the symptoms you listed. There are other things as well but those are the most common I'd think. Hit any curbs lately? ;p
-Xaev