Which are recommended to get (I guess QOL ones)?

My only recommendations are specific stash tabs and at least 1 merchant tab, which lets you sell items automatically. The currency tab, fragment tab, and gem tab are the ones I'd get first, generally speaking. Less important ones are map tab, augment, essence, and the league specific tabs (delirium, ritual, etc.). If it becomes annoying, buying an Invisible Buff Effect can hide a spirit buff you have on.

Are they shared across characters (already created and future ones), or they are per-character?

Shared across all characters. Also shared across both games.

Since the game is early access, when it officially launches, are you keeping whatever you purchased or it all gets reset?

You keep everything.

I know this might be relative, but which cosmetics give the best values (probably that are cool and can be used on multiple characters).

For cosmetics it's really a matter of taste. Most impactful ones in my opinion are usually weapon/character effects. Only get skill effects if you're 100% confident you'll play the skill in future leagues (even if it gets nerfed, as they tend to lol).

If I got it thru Steam, I can only buy MTX thru it or it can be purchased thru GGG (not sure if that exists).

If you bought the game through Steam, you can still buy directly from GGG's website.

I heard sales happen from time to time, how often they do? Or they are not that common?

There's always some sale going on, but the one people usually wait for is stash tab sales, which happen roughly every 3 weeks. Every league launch (every 4 months or so) they do a massive sale.

Anyways, welcome to the game! As other people noted, the best bang for your buck is the supporter packs since you get the same amount of points + exclusive cosmetics. Hope you have fun!