Can you post a pic of your Racer? They might not be worth a ton of money, but most of the time, a 60-70's men's vintage 3 speed Schwinn on Craigslist in Sacramento easily pulls $250 if it is mostly in tact and original. A 50's model would be even more.
If the stock rims are not rusty or bent up, just keep them. Most bike shops around here sell 597 (26 x 1 3/8 x 1 1/4 or S-6) tires for $15 each for a Kenda or CST...gum or black wall.
Old schwinns are very easy to disassemble and reassemble. Just take your time and enjoy it.
If you plan on selling it, keep it as original as possible.