Apple IIGS
The Apple IIGS was the first vintage computer that I ever sought as a vintage computer. It ended up being a Christmas gift from my parents one year, when I was around 15 years old, and it came with just the base system, the monitor, the keyboard, and the 5.25 inch floppy drive. Since then, I acquired a mouse, 2 3.5 inch floppy drives, a 4 MB RAM card, an Uthernet II card, a CFFA 2 card, and a Grappler+ card.
I think this computer captured my imagination primarily because my elementary school had a platinum IIe computer in every classroom (donated by Food World, according to a small plaque on each one). And the IIgs seemed like a weird fantasy machine that added CD-ROM capability and much more modern things to the Apple II line. Keep in mind that the Apple IIe was already pretty obsolete by the time I was using them, so to find out that a machine with any sort of modern utility existed with backwards compatibility was sort of revolutionary to me.