Game crashes out in Windows 7 32-bit during the first mission, does anyone have a solution for this?

Unfortunately, the game has a habit of crashing sometimes on certain machines. I experienced two or three random crashes myself. As they were random, reloading and continuing fixed the issue for me eventually.
Does it always crash (at the same moment) or just occasionally during the first mission?

It seems to be happening at the same point, a few seconds after my only save. I will re-install it and save more frequently. Hopefully this will work. Thanks for your reply.

Since you're in the first mission, that's probably a good idea. Maybe it's only a broken savegame and restarting the mission would fix it too, but it never hurts to re-install at this point. Make sure you don't install the game into Program Files, but into a custom folder like C:\GOG Games\.