This will hopefully touch on all those points.
I first started playing video games in the arcade and on a Sega Genesis at my cousin's house back in 1991. I remember my dad used to take me to a local sports bar called No Frills Grill and they had several arcade and pinball machines; the ones I remember playing the most were Galaxia, Off Road, and an Elvira Mistress of the Dark pinball machine. Now onto my cousin's Sega Genesis. When I was pretty young, my parents used to have a lot of BBQs and get togethers at my Aunt and Uncles house, and while the adults were outside drinking, the kids were in the basement playing the Genesis! I remember playing Hard Driving, Mutant League Football, and my absolute favorite, Sonic the Hedgehog over there. It was Sonic specifically that got me really, really into the Genesis, so much so I convinced my parents to let me stay the night, just so I could play the Genesis longer lol. Of course this eventually led to me wanting a Sega Genesis of my own, and for my 5th birthday my wish came true.
Sadly I didn't get Sonic as one of my first games, but with my Genesis I got The Flintstones (extremely underrated game), Home Alone, and Batman Returns. I mostly played the Flintstones, and also used to rent a lot of games from a local video rental store that has been out of business since probably 1999 called famous Video. I remember renting titles like Joe and Mac, Wolf Child, Mic and Mac Global Gladiators, King of Monsters, and Alien 3 often from there. And of course I rented Sonic, as well as Sonic 2 when it came out. I also fell in love with fighting games via Street Fighter 2 and Tournament Fighter. Lol yeah, I have a lot of fond memories of renting Sega Genesis from that rental store :p. I would get about half a dozen more Genesis games over the next few years, with my favorite being Sonic 3 in 1994, but I don't feel like my love of video games grew from interest to obsession until a few years later on a different console.
The first Nintendo console I ever owned was a SNES I got from my aunt back in 1994. While I loved games like Donkey Kong Country and Doom, I always defaulted back to my Genesis during the 16-bit era. It wasn't until Christmas 1996 when I received a Nintendo 64 along with Super Mario 64 that I fell in love with Nintendo and became obsessed with gaming. I remember being totally blown away by the 3D worlds in Super Mario 64, and it was the first game I ever felt like it never got boring or old. Before obtaining all 120 Stars, I probably put around 100+ hours into that game. Super Mario 64 was only a gateway into the many other amazing N64 titles that I would play and fall in love with. it was during this time when I was fully engrossed in the N64's library that I started to become passionate about video games, subscribing to several video game magazines, going to a local game store for hours just to browse and look at titles, and nearly every penny I earned through chores was spent on video games. I was truly in love.
That love and passion for gaming has continued all these years despite waning at times, but right now it is stronger then ever. So yeah, that is my gaming origins in a nutshell :p