Getting rid of the rust is the easy part. There are a few ways to do it, but an oxalic acid bath is among the cheapest and easiest -- and it'll remove rust inside the tubes, too. Powdered oxalic acid is sold at hardware stores and paint stores as wood bleach. One of my local stores stocks 12 ounce tubs of Savogran brand wood bleach like THIS for about eight bucks. Mix the tub with a kiddie pool full of water and immerse the frame overnight (after stripping it bare, of course). Remove the next day, rinse well, and dry. Optionally, treat the inside of the frame with a rust inhibitor like J.P. Weigle's Frame Saver, Boeshield T-9, or Amsoil Heavy Duty Metal Protector.

Keeping the rust from coming back may be a little more of a challenge. That's an awful lot of bare metal for "touch up". I'm all for keeping paint original when possible, but I'd say you've got a candidate for repaint. Powder coating is another alternative.