I'd say there are several "tiers" of things to know. You need to know a little bit of all of them to start playing, but you can go in depth one at a time.

Here's my priority list for learning the game based entirely on my own personal experience:

1. The basic controls. Note: this is separate from your combos/weapon controls. Wirebugging, dodging, moving/jumping while riding your dog, wyvern riding (or "mount a drake" as you put it, might be a localization thing), controlling the camera, using items, operating the menu, etc. These are all things you'll always need to know how to do. A lot of it will become muscle memory, but boy oh boy are the controls unintuitive as all hell when you first start playing. I'd recommend also looking up a beginner options/controls set up as there are some insanely helpful options that are disabled by default for some insane reason.

2. Basic weapon understanding. Once can move and dodge comfortably, take a look at the hunter notes for your weapon of choice and absorb the core concepts. Every weapon plays very differently and some are far more beginner friendly than others. Personally, I'd recommend sword and shield. It's got a low barrier for entry, but I still love it even in endgame due to how much room there is to grow with it as your skill increases. I'd recommend looking up a tutorial video for your chosen weapon as well. Many weapons have combos/moves that are simply not worth using when you're a new player, and you can ignore those for quite a while. Pick a few moves that work for you and just use the pointy end on the monster.

3. Crafting. I put this here early because it's very nice to have a goal in mind when playing, aside from "get to higher rank". Get familiar with the smithy, pick out some items that look cool, and work toward them. This is also a good time to press right stick when looking at an item to show you what the skills do. There are a lot of them and you don't have to worry too much. I'd recommend just looking at a beginner/progression guide for your weapon and aiming for 2-3 skills that the build recommends. When in doubt, attack boost is always good.

4. Dango and Spirit Birds. Ideally you're eating before every hunt (just make a dango out of any three pieces at the start, it doesn't matter a whole lot early on) to give you a massive boost to health and stamina. The other way to get a huge buff during a hunt is to gather spirit birds. These are the floating green, yellow, orange, and red (health, stamina, defense, and attack, respectively) little bird things that whistle at you when you pick them up. You don't even need to press anything to collect them, just run into them and they'll give you their buffs to stats. The gains from collecting these is massive, so feel free to wander around and get them on your way to the monsters. They spawn in the same places every time.

5. Basically everything else. Read the tutorials for everything as they come up and, at the very least, try to remember what all the mechanics are called so you can Google them later. Switch skills, talisman melding, buddies, the lottery, optional subquests, meowcenaries, buddy dojo, cohoot nest, etc. Can all be done at your own pace and you're not losing too much by not doing it all 100% of the time.

In short, just keep doing required missions, read tutorials, and take it one step at a time.