Just a note here. Having no clue what a Radio Craftsman C500 was, I googled it. Okay, 1950's, obscure brand, built like a battleship, with transformers that look serious vis a vi power output, and factoring in inflation, darned expensive. Apparently these go for around $2,000 now in the far east? The high end collectors in the Hong Kong, Korea, Japan, et cetra region have a 'thing' for really BIG British and American gear from the 50s. Western Electric amplifiers, Tannoy Folded horns that are good foot taller and wider than the K-Horn, McIntosh and Marantz by the ton, Big JBL, Big Altec, Big ElectroVoice, et cetra.
So do consider that the units greatest value might lie in a listing on E-Bay.hk or E-bay.jp before you put a soldering pencil to it.
As for soldering, you'll need a kit of - a good solder sucker (pneumatic spring operated, and one that is easy to disassemble to clean), plenty of spring loaded heat sink/clamps, a serious temperature controled solding pencil/station (Bryan has the name of a good one at a good price), correct electrical flux, and plenty of practice.
Now granted that the Radio Craftsman C500, I assume, doesn't have any printed circuit boards to accidentally fry since it is all point to point soldering. Nevertheless, if Radio Shack still sells little solder it yourself kits (if they don't Gateway Electronics, 2220 Welsch Industrial Court, St. Louis, 63146, 314-427- 6116 surely does and probably has a vastly better collection of solder, flux, flux cleaners, heat sinks, et cetra) get one, solder it together, get it working, unsolder it, solder it together again, get it working again. By that time you'll get a good idea how much heat and time it takes to 1. make solder flow properly 2. how to avoid brittle 'cold' solder joints that are both mechanically and electrically weak. Please note that all solders do have slightly different melting points so if you practice with cheap solder (you should start with this) and then switch to some exotic audiophile solder you might have to re-learn your timing a bit.
There a fellow over on AudioCircle Circles > Special Interest > The Vintage Circle by the name of Bill Thomas who is THE Dynaco rebuilder par excellance. I would read his message strings and ask for his advice concerning rebuilding your C500 before you do anything.
Best of luck,
Ken