A good start would be the beginners guide on /rpg/
https://www.reddit.com/r/rpg/wiki/beginnersguideIf you've never seen how a particular game works and want to get a feel, search around and watch an episode or two of the game online. Rollplay on Youtube has a good channel that covers a lot of different types of games. You can also find games on Roll20's channel as well, and many more on Twitch and other channels.
As for game types, many of the ones listed here are very tailored games meant to play a very specific kind of game. I'll try to give you a summary of some of the popular ones.
Apocalypse World (AW) is a game, as you'd expect, about playing as a group of survivors in a post apocalyptic setting.
Night Witches is a varient of AW about a female bomber squadron in WWII.
Dogs in the Vineyard is a game about faithful 'God's Watchdogs' that go around Mormon-esque towns helping the community and enforcing the judgments of their religion.
Fate Accelerated or Fate Core is a mostly generic system meant to tell a lot of different kinds of stories. Fate Accelerated specifically is a very short and very flexible rulebook for whatever you could imagine.
D&D or Pathfinder are games about playing a group of adventurers in a tolkien-esque fantasy world, generally combat focused but you can play a lot of kinds of campaigns in D&D.
Dungeon World is a 'rules-lite' version of D&D based on the AW ruleset, which basically means it has a lot less rules and is more focused on the collective narrative.
Shadowrun is a game about telling cyberpunk heist stories in a fantasy/cyberpunk futuristic city run by megacorporations.
Blades in the Dark is a game about a scoundrel crew building their gang up from scratch in a city roughly based on the Thief or Dishonored games.
There's many more out there, it just depends on the kind of experience your group wants to have. Many of these rulesets are wildly different and the rules are tailored to create a specific kind of experience. Some of these rulesets are more generic and meant to be used to play a wide variety of games. Some are 'rules heavy/crunchy' which involve a lot more mechanics while some are 'rules light' and deliberately involve much less. D&D, Fate, Pathfinder are examples of more generic rulesets, whereas Blades in the Dark, Apocalypse World, Night Witches, or Dogs in the Vineyard are much more specific.