The original finish does not hide rust. Basically, if there is rust underneath a 50-year-old, very thin paint job, you will see it. Even if you have a few small rust pimples on the surface, don't panic. Rust needs oxygen to form and grow. You can seal the frame with a good car wax, and it'll deprive any rust there is of oxygen. Then it won't grow any further.
The insides of tubes are a different matter, but a refinish will not take care of the inside anyhow. Spraying some of Peter Weigle's FrameSaver probably will stop most rust, because it again deprives the rust of the oxygen it needs. You can do that to any frame, no need to refinish.
Beyond that, store the bike in a dry location. If you ride it in the rain, and if the bike doesn't have fenders, make sure you empty the frame of water entering at the seatpost. (This is mostly to preserve the bottom bracket, the BB shell of the frame is quite thick and not likely to rust.)
Overall, rust is overrated as a problem. Yes, bikes can rust through, mostly due to poor construction, but it is a rare thing to happen, and with proper care, you can stabilize the condition of any bike.
I once had a bare frame in my basement, sandblasted, for 5 years before I got around to having it repainted. During that time, I there was no visible rust forming on the outside, and I didn't protect the steel in any way, not even with wax. This is in Seattle - I suspect Arizona has even less rust.
Bad rust often is caused by the acids of chrome-plating (or stripping chrome) entering the frame and remaining trapped in there. Make sure any frame you have rechromed or de-chromed does not have pinholes in seatstays, fork blades, etc. If after having a frame or rack chrome-plated, you see yellowish fluids oozing from a pinhole you overlooked, it may be best to drill some vent holes and flush the inside of the tube with water first, then with WD-40 to get rid of the water. Then spray FrameSaver inside.
Jan Heine Editor Bicycle Quarterly 140 Lakeside Ave #C Seattle WA 98122 http://www.vintagebicyclepress.com