We had an Amiga 500 (technically it was my dad's, but I am certain I used it more), and I had a Master System II. I'm pretty sure we got the Amiga after the Master System, as I don't remember having them both at the same time.
One thing that I don't miss is swapping disks. I remember the brutal frustration of playing hours of Beneath a Steel Sky when it prompted for disk 15 and I realized that I'd lost it, and couldn't go on. I had to abandon Flight of the Amazon Queen (11 disks) for the same reason. There was a puzzle game, of which the name now escapes me, which had you swapping disks almost every time you changed scene - which you had to do a lot.
In 1994/95 we got an Amiga 1200 with a hard drive (I think it was 20mb). That was a joyous day, because it finally meant no more disk swapping. People these days say how amazing SSDs are compared to hard drives, but the improvement pales in comparison to the jump from floppies to hard drives. Fortunately for me I never had to deal with tapes, as they were no longer being used when I started gaming. I remember my cousins having a ZX Spectrum +2 which somebody had broken off the play button; they used a fork to jam it down.
I feel all wistful over the old days now. Ain't nostalgia a bitch?