It wasn't my first FIFA game, but FIFA World Cup 2010 was an absolute gem. Everything from the music selection, the atmosphere during the game, to the selection globe when picking a team. It certainly defined that summer for me.
This one and 2005. Played it on the PSone and was appalled at how it looked in comparison to the PS2 version. 2003 and 2005 were pretty much the same game on the PSone but it was fun to play with AC Milan when they were still good.
Winning Eleven 6: FE on the GameCube (imported) was the first I really got into. I also had Italia 90 and FIFA 95 on the Mega Drive, then FIFA 97 on PC (indoor football, Q auto-fouls and gets you red carded IIRC).