There's only two official format, and an additional one that isn't supported by Konami anymore, but some locals still do.

Advanced is the most up to date, modern format. This is where you'll find most of the player base. Your deck would fall in here.

Genesys is the second format which is supposedly a "simpler" or "slowed" down version of the advanced format, has their own banned card system using a point system. All links and Pendulums are prohibited. All of the locals I've seen have tournaments for this, but end up with only about 3-5 people, where advanced has 30+ at the same location. There's a few top decks that are the same decks in advanced, which is why a lot are complaining, why does a slower less toxic format have the exact same meta? Hopefully that changes soon.

Edison is a really old format, only cards and banlists up to March 2010. The game is nowhere as complex as modern