Best plan of study for beginner with limited time?

Maybe, from time to time, do some reading from Discovering Chess Openings
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf
or First Steps: the Colle and London Systems
https://www.chess.com/article/view/how-to-understand-openings
or First Steps: 1 e4 e5
https://www.newinchess.com/media/wysiwyg/product_pdf/7790.pdf
https://chesscafe.com/book-reviews/first-steps-1-e4-e5-by-john-emms/
or First Steps: Queen's Gambit.
https://www.newinchess.com/media/wysiwyg/product_pdf/7790.pdf
Be sure to try to use the openings in games in between sessions of learning. Most of the time, one faces a position with no knowledge of a specific move indicated in a book. One has to accept that as part of chess, and think of opening knowledge as a sometimes helpful aid. After a game, it makes sense to try to look up the moves in a book and see if it has some indication of how one might have played better in the opening. Many opening books are part explanation and part reference material. The reference material is included in the text with the idea that one mostly skips it on a first reading, and looks at an individual item when it applies to a game that one has just played. Resist the temptation to try to turn a book into a mass memorization project. There are many important subjects that one should not neglect because of too much time on opening study.
Here are some other reading possibilities that I often mention:
The Most Instructive Games of Chess Ever Played by Irving Chernev (1965)
https://chessbookreviews.wordpress.com/tag/most-instructive-games-of-chess-ever-played/
Winning Chess by Irving Chernev and Fred Reinfeld (1948)
https://web.archive.org/web/20140708093415/http://www.chesscafe.com/text/review919.pdf

Limit the time you spend studying!
Sorry....I'm not trying to be cute....but that is the most obvious solution if you really have limited time for study.
Beyond that though, if it were me, I would focus on studying annotated games of the masters. In other words, a lesson would consist of studying a single game - for as long as you want to spend time on it. You can always stop at some point during the game and return to it later as time permits.
The following article includes recommendations for some good games collections serving the purpose...
Good Chess Books for Beginners and Beyond...
https://www.chess.com/blog/RussBell/good-chess-books-for-beginners-and-beyond
More specifically, I would suggest to focus on games that feature primarily positional-strategic concepts, as well as endgame technique. IMO, you will learn more about how to play better chess by studying games featuring principles and concepts than games that are predominantly tactical in style. Supplement study of these games with books that are dedicated to instruction in positional-strategic, and endgame, concepts and technique. The following blog article may give you further food for thought along these lines, and suggest some possible approaches on what to study...
Good Positional Chess, Planning & Strategy Books for Beginners and Beyond...
https://www.chess.com/blog/RussBell/introduction-to-positional-chess-planning-strategy
As for openings you might choose openings that are "system" openings (King's Indian Attack (KIA), Colle System, London System, etc). That is, openings that feature fairly well-defined themes and plans as opposed to those which tend to be highly tactical in nature and which tend to involve learning lots of so-called "theory" in order to play well (e.g., Ruy Lopez, Sicilian Defense, etc). On the other extreme, you could play openings that become highly tactical extremely quickly, i.e., those that tend to leave "book" very early in the game, for example gambits (Scotch Gambit, Evans Gambit) - in which case there would also be less theory to study.
A third approach to the opening is to study a repertoire book, for White and for Black. For example Vincent Moret has authored two opening repertoire books, one for White, the other for Black.
Specifically, Vincent Moret's "My First Chess Opening Repertoire for White" which I think is excellent for beginner-intermediate players. The author focuses primarily on themes and plans (as opposed to overwhelming you with lots of theory/variations) presenting only enough material to get you started playing the opening quickly. He also does a better than average job of teaching you not only WHAT to play, but also HOW to go about doing it. Very instructive. See my review (as RLBell) of the book on Amazon. Chessable has also created a course featuring both books.
My First Chess Opening Repertoire for White: A Turn-key Package for Ambitious Beginners by Vincent Moret.....
https://www.amazon.com/s?k=my+first+chess+opening+repertoire+for+white&i=stripbooks&crid=2J3VURUGMWFU2&sprefix=my+first+chess%2Caps%2C192&ref=nb_sb_ss_i_2_14
https://www.chessable.com/my-first-chess-opening-repertoire-for-white/course/7543/
https://www.youtube.com/watch?v=f41ZbPq9OpE
https://www.chessable.com/my-first-chess-opening-repertoire-for-black/course/9014/