Most common failure is the generator. Expect to go through four to six in the life of the car. To reduce the number of repeat failures, replace the battery at the same time unless it's less than about two years old. Due to their design, these generators develop huge voltage spikes that can destroy the internal diodes, internal voltage regulator, and can interfere with computer sensor signals causing hard-to-diagnose engine running problems. As the battery ages it loses its ability to dampen and absorb those spikes. GM introduced this miserable generator design in the '87 models. They had a very nice unit through 1986.
You can expect some steering part failures but nothing as serious as what you'll find on most Ford products. Sloppy idler arms will cause steering wander and front tire wear, but they are pretty easy and inexpensive to replace. When aligning this car it is extremely easy to make the adjustments and get them set precisely. That's something the engineers lost sight of on the newer front-wheel-drive cars that are more picky.
If you're looking for fewer breakdowns, I'd rather see you buy an '87 model than anything newer. My daily driver is a rusty trusty '88 Grand Caravan that refuses to break down. I rarely drive my newer vehicles because I know they are more likely to develop problems that I have to fix.
There's lots of little things you can expect to need attention, but almost everything I can think of would cost a real lot more on newer cars when they get unnecessary, unreliable, complicated computers involved in things computers were never needed for before. You will not have to worry about a computer preventing you from operating the power windows, power locks, power steering, heater system, or keeping you from starting the engine from inappropriate activation of the anti-theft system. I envy you.
The front coil springs will sag with age. When ride height is not correct, the suspension geometry will be wrong and the tires will scrub across the road. That results in poor tire wear even though the numbers on the alignment computer appear to be correct. I know a trick to replacing the springs that makes the job fast, easy, and safe, and it's a one-man operation. GM's method requires three people, much more time, and is dangerous. Rear springs can be replaced in a few minutes. The parts are not expensive either.