I started out with the adventure games. The first one I really got to grips with was Colossal Caves. (I dabbled with Zork, but in those days I didn't have access to a computer big enough to run it, and by the time I did, I'd moved on.) I played a number of the Level 9 games – I particularly enjoyed Lords of Time and later wrote an AD&D adventure based on it – and also relished the first three Space Quest adventures. However, I hit the buffers with Space Quest 4, which I thought was just plain silly. How the blazes you were supposed to work out logically what to do with that b****y rabbit in the opening scenario baffled me then and still does so now, and I came to the opinion that if the rest of the game followed this pattern, then I simply wasn't interested any more.
I then went on to RPG games, starting with New Worlds' Tunnels and Trolls. That was OK, but I found that I much preferred the first person view RPG games, especially the Might & Magic series and the first two Eye of the Beholder games. I played those and a few others (e.g. Bane of the Cosmic Forge and Ultima Underworld a number of times, but by then I was running my own business, so time was at a premium and I had to prioritise what I spent it on. I never really got round to exploring more widely. Hell, I even had to cut down on my reading, and for a guy who had been reading on average at least a book a day since the age of 15, that was a real sacrifice!
Strategy games, world-building, and most first person shooters left me cold, although I did enjoy Hexen.