Melvin and cfz -
I agree with John, when you pushed on the basket and altered the vibration, my first hunch was confirmed that the centerpost bearings are worn. Its the top bearing that amplifies the noise, but they're both usually toasted by this point, or have enough play that both need to be replaced.
The agitator shaft I am a little less concerned about - my experience has been that tight centerpost bearings shore up any grooves in the agitator shaft that may cause vibration noises. BUT, if there is a lot of wear on the shaft, it will need to go too because the worn spots can chew up a new spin-tube seal which would be recommended when the bearings get re-done.
If this were my machine I would not be concerned just yet about the motor. I have heard far noisier belt-drives that had good motors, but it is very possible as it was said above that the vibration dampening rubber absorbers in the motor mounts may be dried out, thus transmitting any noise that is there.
I whole-heartedly agree with cfz about the Emerson motors. I have rarely encountered a bad one, same for a noisey one. I have had some wicked GE motors though - these DID transmit unholy sounds through the machine, and when really bad, they will fry the skin on your fingers when touching them, they get so hot. They make good boat anchors at that point. I can hardly remember a 1980s belt-drive that had a GE motor, though they seem to have seen widespread use in early 1970s models.
Good luck with the machine melvin. A bearing job isn't that big a deal if you can get your hands on the right tools.
Gordon