If you have a physical disc, you can verify it's 1.02 by checking the ring on the underside. Look for the code DOL-GALE-0-02
Super Smash Bros. Melee v1.02 is the definitive "standard" for the competitive community and the version you should use for modern play. While v1.00 and v1.01 exist, v1.02 (the "Player's Choice" edition) is the most polished NTSC release, fixing numerous game-breaking bugs and serving as the base for almost all modern mods. Why v1.02 is Considered "Better" Tournament Standard: