Supervised learning

In chess we hunt down chess pieces.

In the beginning we think out of the box. Away from main lines.

At what rating should it be time to memorise the first few moves in the known main lines ?

Kasparov: "A players should study openings as soon as he becomes a grandmaster."
You can get a long way without any opening study: only general principles suffice.
However, you must know basic chess endings and you must train tactics to get anywhere.
Keres: "A player can make inaccuracies or mistakes in the opening, but any mistake in the endgame is fatal."

Not sure what this has to do with "supervised learning", but it is advisable to memorize (and understand the rough idea behind) the first few moves of your preferred openings. Obviously not all the possible lines, but the ones you feel comfortable with.

A good start would be to focus on one opening with white and 2-3 openings with black to be able to properly respond to 1.e4, 1.d4, and 1.c4. There is no rating required to start with that. Surviving the opening until move 5 should be a useful concept even for beginners.

@Toscani

I don't think that we need to look any further than what tpr said.

Opening theory is not at all important; in fact, that same capacity to "think out of the box" is EXACTLY what's needed to create a good chess move, and it's EXACTLY what "learning openings for learning openings sake" will actually help destroy.

Developing a myopic outlook is the #1 chess killer.
The board turns into a "one-way-to-play", claustrophobic, "old-chewing-gum" practice in tediousness.

Stick with the enjoyment.
Stick with the motivation of finding and making the best move.

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Please note:

Opening theory (QGD QID Siicilian Pirc Petrov French etc.) is NOT the same as opening fundamentals!!

Definitely pay VERY close attention to what all of the pieces are doing in the opening.

Definitely understand where their potential lies and design your moves around maximum influence/opportunity/potential.

Definitely be as efficient as possible with every single opening move.

Definitely always calculate exactly what happens if any pawn on the board moves.

Definitely play around with what happens when you do/don't take center.

Definitely play around with what happens when you bury a piece and just decide that, "I'll get that out later."

Definitely play around with what happens when you allow your opponent to have a pawn structure that occupies your side of the board.

Definitely play around with what happens when you move pieces twice that you didn't have to, only to find yourself 1 move short of a vicious combo later in the game. Make the connection.

Definitely play around with the idea of open files and rooks and open diagonals and bishops/queens, and try to understand when they're important to pay attention to.

Do all of these things, and many many more, and learn from your mistakes.

Don't worry about what lines are called. They are good for reasons that the people who invented them fully understand and can make use of...and that's EXACTLY what you need to be doing out there when you're making your opening moves.

Good chess cannot be feigned, parroted, faked, or imitated.

Good chess is a personal and creative process that involves you, the board position, and everything that you can/can't perceive about that board position.

*Chess is YOURS to discover and uncover, Toscani.*

Opening theory is NOT AT ALL important until at least 2200.

Opening fundamentals (putting your pieces on the best squares)? Yes!
Opening theory (Benoni/KID/English/Colle/Hedgehog)? No way.

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What you will find, is that you'll start coming to many of the same conclusion as your chess-predecessors did, but having had approached it from an appropriate angle and PERSONAL perspective, you will have an UNDERSTANDING of the positions, moves, and reasons for them...instead of a myopic disposition that limits your creativity.

@Onyx_Chess

chess is a game before being a selection process with podium confettis. A game should focus on enjoyment or lose the status of game, i dare to think. So i agree with almost all your post (i keep a margin or error, just in case i missed something, or to appear wiser).

Nice elaboration and complement (or supplement?) on previous post.

You can delay your opening theory learning, or you can leap into it immediately. Doesn't particularly matter imo

Chess theory is great! If you have a basic idea for why the moves are being made, I highly suggest getting chess opening books. I became such a better player through memorizing lines.

There is a difference between studying openings on a competitive level and learning how to play basic, well-known lines.

Don't fool yourselves in thinking that Kasparov became a grandmaster, and only then had a look into how the Sicilian is actually played... Opening studies for top-level GMs consists of going through databases, looking for novelties and win percentages.

Starting off by focusing on endgames like every Russian schoolboy is certainly a good approach, but don't assume that all decent players just wing it after 1.e4.

These are the first 20 possible openings for whites first move.
The response for black was taken from the engine cloud analysis and also for the following responses.

The list is only two moves deep. I think it points a player in the right direction without having to go any deeper. The rest is a learning curve.

The plus opening moves are the best first moves to learn first and I memorized them a long time ago.

The rest of the opening moves are for your enjoyment to discover what happens...

A00 Ware Opening = 1. a4 Nf6 2. e3 e5
A00 Polish Opening = 1. b4 e5 2. Bb2 Bxb4
+ A13 English Opening: Agincourt Defense = 1. c4 e6 2. Nf3 c5
+ A50 Indian Game: Normal Variation = 1. d4 Nf6 2. c4 e6
+ C00 French Defense = 1. e4 e6 2. d4 d5
A03 Bird Opening: Dutch Variation = 1. f4 d5 2. Nf3 g6
A00 Grob Opening = 1. g4 d5 2. e3 Nc6
A00 Kadas Opening = 1. h4 e5 2. e3 d5
A00 Anderssen Opening = 1. a3 d5 2. d4 Bf5
A01 Nimzo-Larsen Attack: Modern Variation = 1. b3 e5 2. Bb2 Nc6
A00 Saragossa Opening = 1. c3 Nf6 2. Nf3 d5
A00 Mieses Opening = 1. d3 d5 2. e4 dxe4
A00 Van't Kruijs Opening = 1. e3 b6 2. Nf3 e6
A00 Gedult's Opening = 1. f3 e5 2. e3 Nc6
A07 King's Indian Attack = 1. g3 d5 2. Nf3 c6
A00 Clemenz Opening = 1. h3 e5 2. e3 d5
A00 Sodium Attack = 1. Na3 e5 2. e4 Nf6
D01 Queen's Pawn Game: Chigorin Variation = 1. Nc3 d5 2. d4 Nf6
+ A15 English Opening: Anglo-Indian Defense, King's Knight Variation = 1. Nf3 Nf6 2. c4 e6
A00 Amar Opening = 1. Nh3 d5 2. d4 Nf6

Conclusion: All these openings look like black will take the center if white does not and if white does take the center, then black will take what it can of the center without being attacked. Then on the second move the principle seems to change a bit.

It seems normal to supervise the first few moves. It helps to avoid immediate blunders. The rest is freestyle, a race to gain the initiative and have fun playing.

Thanks for your comments.

@Toscani if you want to avoid immediate blunders, do not invest time into studies of openings that start with an "A00" nomenclature...

Of course, if someone starts with such a brilliant move as Nh3 (which is arguably the worst move possible) then responding with a center pawn is never a bad idea, but that is not a very profound insight... If your only takeaway is to play in the center then good luck playing against the Sicilian or the Dutch.

As I said above, my advice would be to try a few openings, of the "E00" and "D00" section and focus on the ones that suit you. You can easily study those until move 5-10 without much effort and get much more from that.