Rust, your enemy.
The painted underside of the unibody itself is actually fairly rust resistant. You can prevent light surface rust from getting worse by spraying off the road salt and grime in the winter as soon as you can, especially under the car.
However, I've found that the suspension components are much more prone to rusting than the body itself, at least on the 1st Gen cars. The black coating on the stock suspension parts is not bonded well to the metal. It will flake off after many years.
If you catch the rust on the suspension parts or the underbody soon enough before the metal has been weakened or pitted, you can wire brush and clean the parts or panels, and then paint them with a rust-resistant paint or specialty chassis coating. If not, it is a good idea to replace them, and you get better handling too with new suspension bushings.
Eastwood dot com has specialty rust-resistant coatings (and surface rust removers) that you can use after removing all the loose rust and wire brushing as clean as possible. You can also use Rustoleum Rusty Metal Primer and then paint with Rustoleum spray paint or their brush-on paint. Wash the parts or surfaces after wire brushing and before painting if you can let them dry for a few days. Mask off the rubber bushings, exhaust, and other parts before painting.
Beware that all of this is a nasty, very dirty job under the car (unless you remove the parts) and it requires taking the safety precautions outlined in the shop forum safety thread.
In Canada and the northern states, there may still be specialty rustproofing shops, but the underside of an older car likely has to be cleaned very well of the surface rust and possibly sealed with one of the specialty rust sealers before applying rustproofing.