If emulation on PC counts as homebrew, I got into that around the late 90s / early 2000s. Used to play Gameboy, NES, and SNES games on a Windows 98 PC. The only actual game console I had was an Atari 2600 before I turned 12, but I got addicted to Yoshi's Island at a friend's house and just HAD to play it at home. I also was addicted to the Pokemon games, and using a Gameboy emulator I could move my save between Red and Blue so I didn't have to trade to get all 150 (except in the cases of Alakazam, Gengar, Machamp, and Golem.)
I didn't even have internet back then, I had to take multiple floppy disks to the library, and copy games to bring home. With Yoshi's Island, I remember having to use a multi-part ZIP archive so I could span one game across multiple floppy disks. Those were the good old days.
A few years later, I finally got my own SNES and N64. But Microsoft's original Xbox was the first console that I modded for homebrew. I never would have modded it, until the disc drive stopped reading discs. After my mom found out the warranty wouldn't cover it and it would cost over $100 to fix, she told me I could go ahead and rip it apart (I learned to build and fix computers at a young age, and was curious about the Xbox).
I read online about modchips and soft-exploits, and ended up installing the Bert and Ernie font exploits, Phoenix BIOS Loader, Evolution-X, and XBMC (before it turned into Kodi!). Some people here might have experience with this, I didn't have the Splinter Cell or MechAssault games, nor a method of loading an exploit onto a memory card, so I had to hot-swap the hard drive to my PC while booting XboxHDM (Xbox Hard Drive Maker). Upgraded to a 500gb hard drive, replaced the faulty DVD drive, copied all my games on the hard drive and then set up all sorts of emulators.
Since then, I have softmodded a Wii, Wii U, PSP, got a DS flashcart, got an N64 flashcart (64drive by Retroactive), A9LH'd a 3DS, it's all been fun but I'd have to say I had the most fun with the Xbox. Having to chat with an IRC bot so you could temporarily get access to a ftp server loaded with homebrew goodies, good times. For extra credit I ported one of my programming projects in college to the Wii, my professor was very impressed, and it was lots of fun. I really don't have any spare time on my hands these days, but one day I hope to be a contributing developer in the homebrew community.