Good luck. I just reconditioned a slightly newer blue woman's schwinn cruiser last fall.

How you remove rust depends on where that rust is. In some cases you can flush rusty bits out with oil--the pedals and the hubs for instance if they aren't too heavily rusted. I cleaned and repacked the bearings, using new bearings where appropriate and that helped a bit afterwards. Stiff plastic brushes can also help determine where sanding needs to take place. Brush and scrape with a plastic knife any obviously rusted spots to see how deep the rust is. Yeah, sometimes you can just sand and sometimes, if the wheel is badly rusted and appears unusable, remember to save any components, like the hub, in case the 'better' wheel you pick up somewhere doesn't have as good a hub assembly. With vintage bikes you may want to keep any part that is salvageable, or potentially salvageable, around until you no longer own the bike. (I have three sets of handlebars for my ladies cruiser schwinn fer instance; touring, stingray, and traditional cruiser bars. Also, a compatible spare hub I cut out of an older wheel in case I ever do a full overhaul of one of the wheels, etc.)

Note that you can use freecycle.org or craigslist to look for parts for old bikes if you really get into reconditioning.

On the inside of the rim that is worrying you, is it so badly rusted that you cannot retention the spokes? Are there spokes loose in their sockets? If there are loose spokes and you can't retention them, the rim is probably a lost cause. On the inside of the rim, you can also use a wire brush to see how much of the rust you can get out of there. How bad is it precisely? Are there any broken or loose spokes? Or is it worse than that?