I was 3. My Dad had an A500+ at first, but eventually obtained an A2000, an A600, an A1200, and a CD32. The A1200 was the system he focused the majority of his attention on, upgrading and so forth, so that was the one that got the most usage. I tended to use the A500+ or the A2000. The CD32 eventually became mine and, when my Dad moved to Los Angeles, I "inherited" the A1200, which promptly died.
The one logo I can remember the most from my childhood is the Team17 Logo. That and the Title Screen for "ThunderCats - The Game".