Are there recommendable sources on how to learn solving/the concepts of a classic cube?
My two favorite methods are Roux and 3-style.
Roux is the second most common method for speedsolving. Compared to the more popular CFOP method, Roux is more intuitive (in the sense that you mostly solve by thinking rather than by executing memorized algorithms), and requires fewer moves. Roux is much more fun than CFOP, if you ask me, and for adults and/or people who are attracted to the puzzle-solving nature of the cube rather than in learning algorithms and finger-tricks, I think it's easier to learn. Kian Mansour's tutorials on YouTube is a good place to start learning it.
3-style is a method designed for blindfolded solving, but it's a fun way to solve the cube even in sighted solves. It's a very elegant way to solve the cube, based on the concept of commutators. It takes a lot of moves compared to Roux, but the fun thing is that it can be done 100% intuitively, without any memorized algorithms (Roux requires a few, though not nearly as many as CFOP). It's satisfactory to be able to solve the cube in a way where you understand and can explain every single step of your solution. As an added bonus, if you know 3-style, you can easily learn blindfolded solving, which is tremendously fun, and not nearly as difficult as it sounds.
Edit: If you do decide you want to learn, make sure you get a good modern cube. The hardware has advanced enormously since the 1980s, modern cubes are so much easier and more fun to use. There are plenty of good choices. Stay away from original Rubik's cubes, get a recent cube from a brand like Moyu, X-man or Gan.
This is my collection: https://imgur.com/v9OuYNw
Like you, I learned the 3x3x3 in high school via memorized algorithms, and that was only so interesting. Years later my brother got me a Megaminx (the dodecahedron equivalent to the 3x3x3 cube, third one in the top row there) and I was absolutely fascinated by learning to solve that by porting what I knew from the cube. From there I got all those other shapes as well. The most interesting ones to search by name: Dayan Gem 3 (the one that looks like the Star of David), Face-Turning Octahedron (last one in the second row), Helicopter Cube (to the right of the 3x3x4), Rex Cube (right from the Helicopter Cube).
I have hit a wall there personally.
The unfortunate part is that beginner tutorials for Roux kind of suck.
I agree about beginner tutorials. There are some decent Roux tutorials, but they are mostly not targeting complete beginners. I believe it should be possible to make a Roux-based beginner method that is even simpler than the popular layer-by-layer beginner methods most new cubers learn. If you think about it, it seems almost obvious. If efficiency is not a concern, the first two blocks of Roux have to be simpler than the first two layers of a layer-by-layer approach, since you are solving a subset of the first two layers. CMLL is also obviously simpler than the CFOP last layer. The only thing that remains is the last six edges, and that's simple enough that I think beginners could figure out by trial and error. With the right simplifications (at the expense of efficiency) and good pedagogy, I therefore think Roux is ideally suited for teaching to complete beginners. Unfortunately, nobody has done it yet.
It helps also to develop some sort of notation for yourself. This way you can track and repeat your moves.
Solving by layers is kinda logical. So solving one side (first layer) is not hard. Then some experimentation with rotation sequences which temporarily break the solved layer/face and then re-assemble it will lead to discovery of moves to swap the edges into the second layer.
The hardest then is to solve the third layer. Again, the notation and observations help charting your way through.
A curious discovery may be about some repeated pattern of moves which may be totally shuffling the cube yet, if continuing it, eventually returns the position to the beginning state. It's kind of a "period".
Have fun.
In my opinion, it's better to start by solving a part of the cube that still leaves you with a significant amount of freedom of movement without breaking what you have already done. There are several ways to do this. My favorite method (Roux) starts by not making a full layer, but just a 3x2 rectangle on one side. This rectangle is placed on the bottom left part of the cube. You still have a considerable degree of freedom, you can turn the top layer and the two rightmost layers without breaking your 3x2 rectangle.
The next step is to build a symmetrical 3x2 rectangle on the lower right side of the cube. This is quite easy to do by just using the top layer and the two rightmost layers, thus avoiding to mess up the left hand 3x2.
After finishing the two 3x2 rectangles (commonly known as the "first block" and the "second block"), the next step is to solve the corners on the top of the cube. This is the only algorithmic step of Roux, you use a number of memorized algorithms. However, the algorithms are shorter and simpler than those for the top layer of a layer-by-layer approach, because the algorithms are allowed to mess up everything along the middle slice (which hasn't been solved yet) and the edge pieces on the top of the cube.
After finishing the top corners, you are still free to move the middle slice and the top layer without messing up what you've already done. Fortunately, this is enough for solving (intuitively!) the remaining pieces. You can finish the solve by using only these non-destructive moves.
The Roux method, therefore, allows you to keep the maximum degree of freedom of movement (without destroying what's already been solved) all the way until the end. This is what allows it to have a very low move count, and what's makes it easy to learn. It also gives you a lot of creative opportunities compared to CFOP and other layer-by-layer methods. Because of the increased freedom, there are more ways of doing things, and bigger scope for clever shortcuts, especially when building the first and second blocks.
It's not like memorizing algorithms makes it trivial - there's still recognition/look-ahead and finger tricks to learn, if you want to get faster. And finding the optimal cross (in CFOP method) during the 15 second inspection takes some thinking. I'm bad at that.
My son, at age 9, loved learning these kinds of algorithms (he also learned how to solve square roots by hand from a YouTube video and would do random square root calculations to entertain himself, checking his answers against the calculator on my ex-wife’s kitchen Alexa).
For example, it entirely glosses over how to solve the „first two layers“ (F2L) on the left and back faces. It only ever explains F2L for the front and right faces. However, I can’t possibly achieve a „yellow cross“ that way. I wonder why I can’t seem to find any source that actually explains it.
Here's a good beginner tutorial:
https://www.youtube.com/playlist?list=PLBHocHmPzgIjnAbNLHDyc...