My first console was as six switch wood-grained Atari VCS (later called 2600) in 1980 - I could finally play games like Asteroids, Pac Man and Space Invaders at home. Not to mention Combat that came with the console and other classics like Adventure and Breakout. Although I couldn't afford many of those cartridges at thirty pounds a pop.
My personal Atari 8-Bit journey from an Atari 800 (48k) in 1983, and XL (64k) in 1984 and a 130XE (128k) in 1985. Starting with nothing but cartridges, moving to a slow tape drive (15 minutes to load up a game?) and then finally to a 5.25" floppy drive. Atari BASIC was the language of choice along with interesting uses of PEEK and POKE and then some solid 6502 Assembly using the MAC/65 cartridge. I still have a few of those cartridges, including Eastern Front 1941 and Galaxian.
I started with my 520ST in 1986, as well as the many classic games, I also did some of my first C programming with Hisoft Lattice C. As well as using the low and medium color resolutions, I loved my high res mono monitor. I upgraded to a Mega 1Mb ST computer in 1989 before starting University and a year later ripped it apart to put into a custom tower with a very loud fan and hard drive!
My first experience of Arcade games were at the "working mens club" (aka pub) with my parents in the 1970's and 1980's in the UK and then in the USA in 1983 (everywhere from 7-Eleven to Burger King to Supermarkets). Fond memories include Space Invaders, Lunar Rescue, Asteroids, Lunar Lander, Crazy Kong (which I didn't know was a Donkey Kong bootleg), Phoenix, Scramble, Galaxians / Galaga and the continuous innovation that meant often seeing something new. The Golden Age!
In a time before graphics were popular (especially given you had low resolution and limited colour choice :-), instead relying on "interative fiction" text adventures, using natural language input (or at least verb-noun) to interact with descriptive environments. My personal favourites are the Hitchhikers Guide to the Galaxy (on which Douglas Adams collaborated) and the Leather Goddess of Phobos.