I'm showing my age here, but the first console i "technically" had was a GrandStand
I say technically, it was something my Dad owned from his days in the Army. It was my first experience of gaming, and it was a good little machine. Took (i think) those big round batteries (D i think).
I can't remember which way around my first proper console arrived, but i did have both a Gameboy and an NES within a year of each other. The NES i had for Christmas and the Gameboy for my Birthday. Mostly had these because my Dad wanted to play, and the deal between him and my Mum was that he had to share. The Gameboy came with Tetris, and the NES came with Super Mario Bros and Duck Hunt (complete with light gun). I did get a few more games on both machines over the years, most notably Super Mario Land and Dr Mario on the Gameboy.
Somewhere in the 90's, i asked for a SNES for Christmas. However, i ended up with a Mega Drive II instead along with a copy of Columns 2, Super Hang On and World Cup Italia. Went to a local market a few weeks later and picked up Sonic the Hedgehog (complete with the cheat code written on the cover). No complaints with this machine, was the first games console that got me into gaming. Before this, the Gameboy and NES were mostly shared machines for the family. However, the Mega Drive was the first console exclusively for me.
I had other games for the Mega Drive, including Alien Soldier, TazMania, Toy Story and Aladdin. I had borrowed Sonic 2 along with Sonic and Knuckles from my cousin around the time he got a PlayStation with Tomb Raider. Can't say i missed not owning a SNES at the time, i was having a lot of fun with the Mega Drive. However, because i had the Mega Drive, the Gameboy and NES became my sisters. And she was not happy with sharing, and the urge to play Nintendo creeped up. I was around the age of getting pocket money, and around the time of my birthday, i had saved some of it up and along with some birthday money, i nabbed myself a Gameboy Color
Because of my sisters selfishness, my parents took her copy of Pokemon Red and gave it to me to go along with it (she kept Blue), i had also picked up a copy of Link's Awakening and re-acquired Tetris from a box in the attic (i did eventually get all the Gameboy games back when she threw them in the bin one day). This was my own Gameboy, and i got my urge filled for Nintendo. Because of this, i asked for an N64 for Christmas of 1999.
I got one, along with Ocarina of Time and Super Mario 64. Both these games alone was more than enough to last. It was around this time i had a paper round, so was able to buy the odd game here and there (wasn't a regular round, more cover for someone as and when). It was also around this time i discovered that N64 games were expensive, so quite a few of my games came from Gamestation's pre-owned area. The likes of Mario Kart 64, F-Zero X and Turok 2 were fine examples which cost me a couple of pounds instead of mega bucks. The first N64 game i got new was Banjo Kazooie, which i got from my wages on the odd round. Only a players choice copy, which wasn't expensive (that range of games was a godsend at times). Majora's Mask followed in 2000, and so did Donkey Kong 64.
Ended up with a copy of GoldenEye and Perfect Dark down the line (Perfect Dark was from a friend, he got bored of gaming. GoldeneEye i got at a carboot sale)
The N64 was the era where i got into my gaming magazines, of course it was N64 magazine i purchased. It was here i learned about E3 and the gaming world itself, so i knew when things were coming out. More so, the GBA and GameCube, both machines i had a keen interest in getting.
When i did get a GameCube and GameBoy Advance, these 2 machines were the last ones i got from my parents (well, they contributed to the GameCube, i got the GBA). They nearly got me a Dreamcast, but went to the Nintendo route (and i guess i was lucky as the Dreamcast ended Sega's console business soon after).
The rest as you say, is history. I did get an Xbox 360 (the first non-Nintendo machine since the Mega Drive) over a Wii as i wasn't happy with the route Nintendo were going after the GameCube. The 360 introduced me to the world of Online gaming (and the price tag). I did get a Wii though a year or so later, but this era was the first era of owning 2 home consoles over just the 1 and a handheld. Have owned a DS, 3DS and WiiU for Nintendo (can't say no to the Big N).
I would have got a Xbox One, but the last straw was E3 2013 (i was growing tired of the 360 in the last 2 years leading to this, with their focus on media and Kinect coming through). So for the first time, i got a PS4 and have loved it. Unlike the 360, where i had 3 consoles in it's lifetime (Premium, Elite and Slim), the PS4 i have is the launch model i got nearly 6 years ago and it's still going strong. And over a year ago, got a Nintendo Switch which rekindled my Nintendo love again.