I bought the original PlayStation for my younger brother for his birthday in June 1997 with money from my first job. I actually debated between buying the PS or a Virtual Boy which was on display at our local Toys R Us. But, the "Clearance Sale" tag already hanging off the Virtual Boy display was enough of a warning flag to steer me away (I actually thought the red LED graphics were cool for its time). We already had an N64 (and every Nintendo console before it), but we were also huge fans of the Final Fantasy series. Having played Final Fantasy on NES, and Final Fantasy II and III (as they were named in NA) on the SNES; we were bummed to learn of the rift that formed between Square and Nintendo over the N64's cartridge format. So, once Final Fantasy VII released to acclaim on the PlayStation there was no question that would be the first game I would get for the system. That game actually got me into a bit of trouble at work later. When I got near the end of the game one Saturday night, I stayed up all night finishing the game. I never woke back up in time for my Sunday morning shift. Fortunately, my manager liked me enough that he covered for me and told our boss that I had called out sick.
I also purchased Vandal Hearts that very same day, so that we would have more than one game to play. A very cool tactical RPG that we also enjoyed very much. So, technically, they were both first.