Well, I only remember seeing SF2 once or twice in an arcade, never played it before. I did not like fighting games too much when I was little. (mostly because some random high school/college student would always RAEP me without mercy)
First games that I played and enjoyed
were Super Smash Bros was Tekken 3 and, later, Tekken Tag Tournament.
First 2D game was KoF 1998 or 2000 (can't remember exactly). I sucked at it big time. First 2D game I liked was Melty Blood Act Cadenza