My first real experience with home computers was my big brother's Commodore 64. For the first few months he had it hooked up to an old black&white TV, but it was still brilliant. I mean, he rarely let me play it of course, but I was tolerated hanging around in the background occasionally, while he played Samantha Fox Strip Poker or California Games or Boulder Dash with his mates.
A few years later I finally got my own computer - an Amiga 500. With a RAM expansion and a proper monitor! Some of my favourites were Stunt Car Racer, Pang, Lotus Turbo Challenge 1 and 2, Sensible soccer, Pinball Dreams/Illusions, Civilization, Bundesliga Manager, North & South, Super Cars and many more. What a fantastic machine that was!