Uhm... quick summary of regions:

LMS: Catch them on twitch, not sure if they can be found on youtube... Taiwanese region, two powerhouse teams and the rest sort of like minion teams...

LCK: Korean league. Top 3 here are usually the best teams in the world (these other four leagues you can catch on youtube if you follow lolesports.com). They're elite in skill, tactics, and pick/bans. They fight less than other regions on average and don't make errors very often.

LPL: Chinese region. Funny casters. High amount of skill and exposition of that skill. Very aggressive league, a lot of kills, a lot of team fights and skirmishes. Elite in skill, team fights, good in pick bans (and entertaining)... a lot of inner-team drama in that league, too.

NA LCS: North American league. High production value. A lot of mistakes, a lot of fights, a lot of kills. Entertaining games. Tactics and pick bans iffy. A lot of drama in fans.

EU LCS: European league. High skill in midlane. Strong tactical league. Not too much animosity. Not as much aggression as other leagues (unless you're watching certain teams). Pick ban tactic on the iffy side.

Every league has legacy teams/players, and you'll learn them over time. If I was you, I'd pick one or two of these leagues to watch based on what you'd prefer to watch (you can try them all).

For MSI and World's, they hold international wildcard competitions for teams coming from other regions to slot their last few teams.

The calendar is like this: Jan-Apr - spring split, May - MSI, June-Aug - summer split, Oct - World's(most popular), Dec - All Star's. During the year, they have a few other international competitions, "IEM" chiefly...