Although we owned many kinds of computers in my family, our first true personal computer was the CompuColor II. http://www.computercloset.org/CompuColorII.htm
My dad purchased it at a computer products show in 1981. At the time it was superior to both the IBM PC and the Apple computer. At only $5,000 it wasn't cheap (remember - this was 1981) but it sure was fun.
It came with 4K of RAM and a 8" floppy drive for storage. Eventually we upgraded it to the maximum of 48K and installed an external floppy drive for more storage. There were some great games, including one where you had to fire mortars at another gun that was placed on a hill. You needed to compensate for angle and windspeed to successfully destroy the other side.
What was your first computer?