Godot

I don't know how much programming experience you have so I won't assume yet the stuff I wrote down the line are quite basic.

Generally speaking you always want to use the latest stable (!) version of whatever tool you want to learn, just be sure you're watching/reading tutorials for the right version.

As to how to learn, I'd suggest to start with videos on YouTube - get some free assets on itch.io (maybe ones being used in the tutorial, maybe not) and just do stuff along the videos - figure out the basics, build the base and move from here.

You want to get the feel of the process, what works, what doesn't, try to break the whole game in pieces and just do one at a time. Make an animated character, make a level with collision, map some inputs to the character, run through the level, add something the character can break, add means to attack, break the thing that is breakable, add an enemy, realize there's no health, add health and damage and so on... Don't really focus on getting it right - focus on getting it done, you'll have a lot more understanding how to do something better after you've done different parts of the game.

As to the docs - it's great, but you don't need to read it as a book to start something, it's a hefty time investment and you won't get much out of it at the current point. Just remember that the doc exists and go there with questions you have. You're stuck with the collision BS? Go read the docs - the answer is there and you'll understand and memorize it much better as you apply it to a problem you've faced.

Also don't be disappointed or harsh on yourself for being "stupid" and doing something in a weird/ugly/inefficient way after learning how it's done properly - it's part of the learning process.

For the publication of your game - it's up for you to decide, I mean you can just share it with friends or relatives, it's all good as long as you're having fun with it.