I'll show you the steps I took to strip it all down and refinish it. While I can't technically call this a restoration (because it wasn't returned to its original state), it looks good and is functional--which is what I was after. My kids now have a shiny new-looking wagon that will hopefully hold up to many more years of use.
It took a little time and attention but this wasn't a terribly difficult project. If you have an old red wagon that needs a little love, perhaps you can get some useful ideas from this. Thanks for taking a look.
Step 1: Disassemble wagon
I began by removing the complete wheel assemblies from the wagon bed and disassembling the pivot plate and handle from the front bolster (the axle and support structure).
You can purchase new wheels and hub caps as well as most other parts for current wagon models at Radio Flyer's website. If you need to remove the wheels, this page on Radio Flyer's website has instructions on how to remove the hub caps. Note that they get destroyed in the process. If you're restoring an older discontinued model, finding parts may be a little more tricky . . . but there's always eBay.
Step 2: Strip bed
I used a wire wheel on my power drill to remove the rust from the inside of the bed and knock off any loose paint. After this I used paint stripper to remove the majority of the remaining paint.
After using the stripper I went over the entire bed with the wire wheel to remove any last bits of paint, and to grind down rust spots as close to bare metal as possible.