Hi there. I had installed the GOG copy of Gothic 1, as well as the player kit and the Classic System pack. Installing them makes the game crash right after it starts up. What should I do?

The game crashing could be caused by anything really.

Make sure:
-that you have installed (as admin) to a directory that's not on your system's c:\ drive (which eliminates potential issues like not being able to save)
-that you have installed (as admin) in the recommended order: base game, patch 1.08k, playerkit 1.08k and system pack 1.8

If it's still crashing (try to run the gothic.exe as admin too) it still could be because of all kinds of other things (other programs/services interfering, your anti-virus application being overzealous, your version of OS missing certain dependencies, etc)

Contacting support and providing them with the necessary information might be your best bet at this point.