Major pitting in bearing cups; what can I replace?
You should replace the balls for sure.  They're cheap, readily available (from any bike shop -- just take in a sample ball), and would very likely solve most of your problems.
You can also fairly easily replace the cones.  You might have to order them, but they should be reasonably inexpensive.  You may want to replace the axles at the same time (they often come as a set).
Replacing the cups would require replacing the hubs, and, if you hire it done, this is usually more expensive than just replacing the wheels.  But you can likely get several years of service out of the bike with the existing hubs.