I had a whole bunch of generation 2 VW's.
What RallyJon has to say is all on the money, just a couple add's
In 1987 there were both 8 valve and 16valve GTI's.
Things to look at are:
Front motor mounts- They wear out quite quickly and when they go bad the engine rocks far enough to break the cat-exhaust manifold seal. Easy fix for 8V. If the car is a 16V it will be a bit pricey as you will most likely have to purchase a new downpipe.
Timing belt on 16V. When they break pistons hit the valves.
The 8V will just spin if it breaks. No interferance.
Easy timing belt replacement- 16V's can be done in under an hour for sure.
16V distributer- It's mounted sideways right off the cam and the oilseal leaks soaking the distributer. Easy fix.
8V distributer- Make sure the Hall effect sensor isn't cracked off and held on with a zip tie
Shifter linkage. Just like a 911. Do the bushings and adjust correctly. Lot's of old VW's shift sloppy. Also you should have to push the lever down to get in reverse. If you dont have to the PO hamfisted it and broke a little 2dollar clip under the shifter. (easy fix)
Synchros, in the trans. Sometimes shift a lil crunchy, especially 1-2 gear.
An 87 GTI should have rear disc brakes. Make sure they're not seized, they often are.
If the car idle's a bit rough see if the dipstick collar is broken. Owners often overlooked that.
Is the floor wet? The plastic sheet behind the doorpanel is gone or ripped.
I know I'm forgetting alot but generally these are good reliable cars but in no way a "put gas and forget" kinda car
Here was my favorite 87 GTI
