The first console system I could afford to buy myself was the PS1.
Got it when I was working to play games like Raiden Project, Resident Evil, and various ported-from-arcade shooting games (Gunbird, 1942, Strikers 1945, Kyukyoku Tiger, etc).
Later on, I also got a Neo Geo MVS board (the arcade board, with an adapter to hook up to a TV), with mainly Metal Slug series (my favourite on the Neo Geo) and some of the KOF (alll these are the arcade carts (much cheaper than the home carts)).
When the home Neo Geo price dropped (probably due to emulators), I got one but I never really played much with it. Some people say the Neo Geo joystick is big, but it's nothing compared to the Hori Real Arcade Stick.
Nowadays I don't have much time for console games, I prefer to play emulators on my PC or play with my DSL when I'm outside.