Excellent question! As a 2116 USCF rated Golden Knights correspondence player from the pre-home-computer '70's who is AWFUL with short clock times, and who knew enough to coach a high school team to the point where it gained "elite" status in the state, and who has an advanced teaching certificate and has developed course curricula. I looked at what I would do - and where the holes are in my chess understanding and determined where I should start when I returned to chess after nearly 2 decades away from serious chess. If I was a starting chess player (none of my book recommendations are absolutes - there are a lot of alternatives for each one):
1. Learn the Moves. The Alburt and Pelts book, Comprehensive Chess Course, Vol 1 (12 lessons) is excellent in that you'll finish it knowing all the basic points (en passant, etc.) as well as how to open the game.
2. After learning the moves, I would get a basic understanding of all phases of the game from studying two books:
A. Capablanca's 60-page book, Chess Fundamentals. I wouldn't be close to knowing it all, but I'd know what things I had to learn: openings, tactics, strategy, endgames are all in there.
B. Then, Albert and Pelz, Comprehensive Chess Course, Vol. 2, From Beginner to Tournament Player would make me ready to challenge lower-rated tournament players
3. TACTICS including their PATTERNS: the key things that separate winners from losers and players who can play fast. At this point studying tactics and playing games should be the majority of what I do. While studying the books in step 2 - and continuing through the future steps.I would start working tactics puzzles at least an hour/day when time permits. The ones here at chess.com are excellent and so are those at chesstempo.com. I would also study a book like Dan Heisman's Back to Basics: Tactics.. Also, since videos use an additional sense, hearing, stuff like Dan Rensch's "Patterns You Must Know" at chess.com or similar YouTube videos helps. So do clubs where NM's, etc. are invited to speak.
4. I would read How to Open a Chess Game by Larry Evans and 6 other GMs. This is more important than looking in-depth at any one opening. Last week, I played the Caro-Kann as Black and after 1 e4 c6 2 Qf3 I was out of the books! Having studied Larry Evans saved me!
I would also make it a MINOR point to begin building a repertoire as I also worked on tactics and the steps to follow. As White I would play I e4 and, since beginning players have difficulty with closed, cramped positions and I'd want to steer away from opponents who've memorized a lot of book and know a lot of traps I would suggest:
A. vs 1...e5: the Bishop's Opening or Vienna Game
B. vs 1...c5: the Closed Sicilian (closed but not cramped: White claims a lot of space after 2 Nc3, 3 g3 4 Bg2 then usually 5 d3, 6 f4.
C. vs 1...e6 the French Advance
D. vs 1...c6 the Caro-Kann Advance
E. vs anything else: standard principles.
As Black:
A. vs 1 e4: 1 c6, Caro-Kann, IF I can handle it vs lower-rated computer opponents and then human online opponents. This is mainly so I can get my QB outside the pawn chain, have a pawn structure/N-outpost plan, and am not cramped. If I can't handle it yet, I'll shift back to 1...e5, learn how to deal with the King's Gambit and Fried Liver attack and just use the N's before B's, castle early, etc. principles to get me to a playable middlegame.
B. vs 1 d4 or 1 c4, 1...c6, 2...d5 the Slav Defense, where, again, like it's cousin the Caro-Kann, I get my bad QB outside the pawn chain to f5 or g4 before blocking it in with e6. This is less cramped than Q's Gambit Declined and less initial positional knowledge is needed than the Indian Defenses. Note that 1 d4 c6 2 e4 transposes to the Caro-Kann so, as mentioned above, I need to know something about it even if I don't regularly play it.
5. Endgames: I would get any of the major endgame books. Fine's old Basic Chess Endgames was easy for me to understand 40 years ago and the cheap paper in its paperback is slowly turning brown on my shelf - but it still works! Today, I prefer Silman's Complete Endgame Course from Beginner to Master because it gives me a structure of what I should study and what things I should review at my level.
6. Strategy. I would study Silman's 658 page How to Reassess Your Chess, 4th Ed. and complete the problems in the 423 page Reassess Your Chess Workbook - which can be done with any edition of the main book or without it to some extent because part of the main book are repeated in the Workbook.
I would also study Keres & Kotov's The Art of the Middlegame. Chapter 2, "Strategy and Tactics of Attack on the King," written by Kotov is the best 50 pages of chess instruction I've ever read.
Seirawan's "Winning..." series, especially Winning Chess Strategies, Winning Chess Combinations, and Winning Chess Tactics are good alternatives for any of the steps here.
7. Thought Process. Reaching this point, I'll be wondering why I overlook moves, why I get lazy in analyzing certain positions, why i let my clock time run low, etc. (I STILL need to improve here in real life!) and I need to learn at the highest level of learning: self analysis of how my mind works.
This is where the books by Dan Heisman shine. Everyone's 2nd Chessbook has thinking embedded throughout it's 117 pages. A Guide to Chess Improvement: the Best of Novice Nook has a 70 page chapter on Thought Process and a 9 page chapter on Time Management. The World's Most Instructive Amateur Game Book is a fantastic idea: it shows you what players do WRONG and what they should have done RIGHT instead of those game collections that show you what Grandmasters did at a level far beyond my level of chess understanding.
Fun little experiment I thought I'd enjoy hearing input from the community about.
Pretend you just started playing chess. You were passionate about learning the game and getting better.
What opener would you play as white? What about as black for e4 and d4? Why those openers? How would you study them?
Which tools would you use to develop your tactics? Why that tactic problem generator over another?
What books would you read first? Why those books?
What time control would you play the most at? Why that time control?