Can't shake this shaking feeling

I can't decide if it is my engine or my tires that are making my car shake . . . or possibly both.

Here are the symptoms:

I notice the shaking mostly between 30-40mph, but I can also feel it at higher speeds, just noticeably less.

It is more noticeable when I am accelerating than when I'm braking.

No noises from inside the car. When I listen with the hood open, the engine doesn't sound as smooth as it used to. I posted a video so you can listen and see for yourself. http://www.facebook.com/video/video.php?v=458809010539

I recently replaced the distributor. There was a whole different post for that project. You can check HERE to see what I did, but it may only be important to know that I did not set the timing. I went to AutoZone to buy a timing light and the guy said he didn't feel right selling me the only one that would work for my car because it was $100. He said that I should be fine, since my car was running well. Since then, it has gotten progressively worse. I have adjusted it a couple of times to experiment, but there is still the shaking.

As for my tires, I recently had a flat after a very long road trip. I replaced the front driver's side with a spare that was in the car. I bought this car at an auction almost a year ago, so I have no idea what its condition is. It seems okay, I had it balanced and I am trying to wait until I can afford winter tires before I replace it.

Here is a pic of the spare:
(BF Goodrich Radial T/A)

Here are the other tires:
(Prime Well PS850)


Any suggestions before I take it in to the shop?