Depends on your definition of your, and computer.
First thing that involved a computer was my older brother's Atari VCS. We had a 4 switch woodgrain one as far as I can remember.
First computer I used was, like most american public school students in the 80s, an apple ][. Dunno if it was plus or e or what, but it was one of those beige wedges.
As I became more fascinated with those beige wedges, I started wanting one of my own. My parents tried to placate me; first with a Vtech learning window (which was fun, but limited, and I promptly lost the cards) and a Vtech Socrates a few years later. (A tremendously bad deal, BTW; at launch, it cost the same as a XEGS, which would have been more useful, fun, and educational; the only thing I could stand doing on the Socrates was drawing.)
Between the LW and the Socrates, I got a NES for my birthday. First thing with a CPU in it that was mine. Also during that period, I encountered the first and only Commodore PET I ever used.
Finally, my parents caved. My middle school had 2 computer labs, one with networked IIGSes, the other had networked PS/2S. I thought the IIGSes were better, and asked for one. Dad goes to the store and brings home... a Packard Bell 386SX. VGA, 2MB ram, 1 each of 3.5 and 5.25 drives, a hard drive, and a built in speaker. Family's first computer.
It had... issues. Enjoyed QBASIC and a few games; Castles 2 was a favorite. Did word processing. It had a very simple GUI that was really just a DOS launcher. There were constant, but minor, problems.
A decade (and another PC) later, I bought parts for, and assembled, my first computer. It was an AMD based PC system, that used socket A, IIRC. Windows 98. It was pretty awesome.