It's a bit weird the default GOG setup seems to rely on ancient 3DFX Glide for graphics, for which the hardware has been gone so long that it has needed an emulator for nigh on a decade and a half. The game seems to run just fine with D3D or OpenGL graphics. With D3D there is a lot of lag in the build menu for me, but with OpenGL everything seems just peachy at 1600x1200.
Now, what really was a merry goose chase is how to get into OpenGL graphics mode, since all I had was a little black square at the top left of my screen after the 3DFX logo. The key is starting the game in software rendering mode (so without any hardware graphics support), which can be done by creating a shortcut to cataclysm.exe, opening its properties and adding the /sw switch to the end of the target field. This will allow the game to launch so you can get into the menu. In the menu you can set up the 3D graphics mode to OpenGL and set it to your preferred resolution. Then exit the game and start it with the default exe (not through the shortcut you created, nor GOG I think). Haven't had any problems like this with it so far up to mission 4.
I've been toying around with some settings in the process, so you also might need to set compatibility mode to Windows XP (Service Pack 2) like I did at some point. That'll cause the game to run as administrator somehow, I couldn't care less myself, but you'll know you can expect the elevation popup then. I've also tried messing with the registry settings to get a widescreen resolution going (1920x1080) and while that seems to work rendering-wise, it screwed up the mouse cursor & interaction for me, ymmv.
Good luck!