diagnose clyde's car

[clyde]

Symptoms:

1. At any speed or road condition, steering wheel may begin to vibrate lightly, then builds up to pretty severe shaking within a short period of time (seconds as opposed to minutes) and doesn't stop until the car comes to a stop. Intermittent. Happened once about a month ago and didn't repeat until tonight. Takes a few miles of driving after the car has stopped for a period of time to start when it happens at all.

2. There seems to be more play in the steering wheel at center than there used to be, particularly at low speeds. Sometimes, but not always.

I haven't jacked the car up to shake the wheels (too late, too cold, too lazy). Not sure if there are any noises.

First thing that comes to mind is tie rods/ends. Then CV joints. Then steering rack. Does that sound right?