The first console I ever played/"owned" was the Sega Genesis. Owned being in quotations because it was technically my older brother's. The first video game I ever played was Mortal Kombat on said Sega Genesis.
Home console was Spyro the Dragon on PS1 when I was 5 or 6.
Although I did play on the Gameboy before then and while I remember a selection of games (Metroid II: Return of Samus, The Legend of Zelda: Link's Awakening, Taz-Mania) I don't know which one was "first".
My first console I owned was a SEGA Dreamcast. The first console I played was the SEGA Genesis. I believe the first game I owned was Sonic Adventure and the first one I played was the first Sonic game.