I removed the decaying plastic (or very old, thin rubber?) grips, and found a mess of cardboard, or paper, or cork, or something underneath, which is proving difficult to chip off.
Here's a photo of the small spot I started on the handlebars, which also shows the poor shape they're generally in. Still, I got this much done with just a touch of oil and the steel wool, so that's encouraging.
The front hub and rim are shining up beautifully. I only just got started, so I didn't take a photo, but they will fairly gleam when finished. The front hub has apparently been serviced somewhat recently, too, since the bearings are still well-greased. All-in-all, I'm still pretty encouraged.