I was a SNES owner and had my eyes across all the upcoming consoles of that time... there were a lot actually (32X & derivatives, 3DO, Jaguar, CD32, even Neo Geo CD). Half of those never made it to Australia or if they did, not many of them.
So realistically, it was always going to come down to N64, PSX and Saturn. At first, Saturn and it's arcade ports were tickling my fancy. But Australia again... it was only at a few retailers initially, and it was something like $800 AUD. I think PlayStation was $700... don't quote me on these! Then one day I saw Daytona in the flesh, and on a dpad, with those graphics... it just wasn't doing it for me like i'd hoped (I should add, nowadays, it's Saturn that i have the most games for!). PSX was getting all the buzz and was cheaper.
But i couldn't afford either in reality, so unfortunately i traded my entire SNES collection to fund that PSX. My first game was DOOM. Lots of my friends said WHY at the time ... but i didn't have a PC, and so i really wanted to play it, and of course it was great!
The demo disc was my poison though. Wipeout first and foremost, Destruction Derby, Toshinden and even Loaded were so new. And the trailers for Ridge, Tekken and so on... But i never really had much money, so I hired games mostly, i think i only bought Ridge Racer Revolution, Wipeout 2097 and Street Fighter Alpha.
I loved them all, but it was the lack of Nintendo games, and perhaps the regret of trading in my SNES... and of course, lack of cash... that forced me to trade the PSX, so i could buy an N64. This was of course after playing Mario 64 at a demo truck they had going around town.
Over time, some of my friends got their own PlayStations, and so I experienced most of the big PSX games like Resident Evil, FF7 and MGS. I kept playing Wipeout and Street Fighter Alpha series with my friend for years too. Over time i went back and played some more of the classics, most memorable would be SOTN.
In retrospect, the variety on PSX made it more like the SNES 2 that i wanted, than the N64, so there was still some regret at trading in my machine. Thankfully with more money later in life, i haven't had to trade in anything since those days!