Take it to a lbs (local bike shop) that specializes in restoring old bikes to rideable condition. Anywhere else will try to talk you into a new bike. Lurk on th Commuter sub-forums for all the info you can get and most importantly RIDE. Everything else will fall into place. One can avoid a certain amount of the difficulty in the trial and error method, but the satisfaction of toughing it out soaked to the bone through a rainstorm will build an inner strength unlooked for. Your Wal-Mart bike is fine. Probably just needs a tune-up including truing of the wheels. Ride it and as your experience grows your taste will change. Good luck!

Btw, 22 miles rt is a solid commute of approx. 4400 miles per year figuring a 4 day per week commitment @ 50 weeks. That's layin' it down my friend. Good on ya!