Odds are, if there is something in particular you want, you're in the right place. A want ad in the classifieds will get you some answers. If you're just looking for any old bike, keep watching CL. I checked out of curiosity, and the only thing that came up were a Bird Thunderbird and a Manco Thunderbird (not at all related). Both seemed a little steep for an initial investment.
What sort of riding are you wanting to do? On road or off-road? Do you want full suspension, half suspension or a rigid frame? Big tire or small tire? Big bike or a small bike? I've owned an array of bikes and I've found that if I'm actually going to ride it, I need it to be a larger frame with either full suspension for my back's sake, or have larger tires that absorb some of the shock when riding off road. It all comes down to personal preference.
Some bikes are easier to find parts for too -- ARCOs and Birds seem to be plentiful. Cats do too, but some parts are really difficult to find (footpeg covers, clutch cover, etc). Some are really desirable and normally command a higher price, like Rupps or Bonanzas. I suggest doing some research and find the one that best fits both your ass and your budget. Doing a true restoration can put you in the poor house on the wrong brand or model.