1999 Saturn SW1 tire or alignment problem - or worse?

First of all, I'm not sure if my Saturn is 2 wheel or front wheel drive, I just guessed.

My problem started within the last week or so. At first I actually thought it was the roads I was driving on. It felt like there were "ridges" in the road, so my car slightly shook as if it were going over bumps. Now I know it is definitely my car! My car is shaking (shimmying) and pulling to the left. I know for a fact that my tires are very old and need to be replaced with new ones. I plan on doing that this payday. Will that with a front end alignment fix my problem, or could it be something much worse (and more costly)? Your advice is very appreciated!