Whats the best way to study a new opening?

memorize all the moves and variations?

Most of this was prepared while thinking in terms of someone with a somewhat lower rating than yours. Perhaps some of it would still be of interest. My guess is that, even with your rating (somewhat higher than mine), it would still not be a good idea to attempt to memorize all the moves and variations. Anyway, here is the stuff:

https://www.chess.com/forum/view/general/video-on-openeings-for-beginners

https://www.chess.com/article/view/the-principles-of-the-opening
"... For beginning players, [Discovering Chess Openings] will offer an opportunity to start out on the right foot and really get a feel for what is happening on the board. ..." - FM Carsten Hansen (2006)
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf
Once one has chosen openings, I think that there is wide agreement that the way to start is by playing over sample games. Some of us think that it can be useful to use books like First Steps: 1 e4 e5 and First Steps: Queen's Gambit
https://www.newinchess.com/media/wysiwyg/product_pdf/7790.pdf

https://chesscafe.com/book-reviews/first-steps-1-e4-e5-by-john-emms/
https://www.newinchess.com/media/wysiwyg/product_pdf/7652.pdf
as sources of games with explanations intended for those just starting to learn about an opening. 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.
https://www.chess.com/article/view/learning-an-opening-to-memorize-or-understand
https://www.chess.com/article/view/3-ways-to-learn-new-openings
https://www.chess.com/article/view/how-to-understand-openings

https://www.chess.com/blog/HanSchut/understand-your-opening-using-tabiyas-pawn-structures-model-games-and-typical-tactics
"... Overall, I would advise most players to stick to a fairly limited range of openings, and not to worry about learning too much by heart. ..." - FM Steve Giddins (2008)
"... I feel that the main reasons to buy an opening book are to give a good overview of the opening, and to explain general plans and ideas. ..." - GM John Nunn (2006)
"... If the book contains illustrative games, it is worth playing these over first ..." - GM John Nunn (2006)
"... the average player only needs to know a limited amount about the openings he plays. Providing he understands the main aims of the opening, a few typical plans and a handful of basic variations, that is enough. ..." - FM Steve Giddins (2008)
"... Everyman Chess has started a new series aimed at those who want to understand the basics of an opening, i.e., the not-yet-so-strong players. ... I imagine [there] will be a long series based on the premise of bringing the basic ideas of an opening to the reader through plenty of introductory text, game annotations, hints, plans and much more. ..." - FM Carsten Hansen (2002)
https://web.archive.org/web/20140627055734/http://www.chesscafe.com/text/hansen38.pdf
"... The way I suggest you study this book is to play through the main games once, relatively quickly, and then start playing the variation in actual games. Playing an opening in real games is of vital importance - without this kind of live practice it is impossible to get a 'feel' for the kind of game it leads to. There is time enough later for involvement with the details, after playing your games it is good to look up the line. ..." - GM Nigel Davies (2005)
"... Review each of your games, identifying opening (and other) mistakes with the goal of not repeatedly making the same mistake. ... It is especially critical not to continually fall into opening traps – or even lines that result in difficult positions ..." - NM Dan Heisman (2007)
https://web.archive.org/web/20140627062646/http://www.chesscafe.com/text/heisman81.pdf
"... Once you identify an opening you really like and wish to learn in more depth, then should you pick up a book on a particular opening or variation. Start with ones that explain the opening variations and are not just meant for advanced players. ..." - Dan Heisman (2001)
https://web.archive.org/web/20140626180930/http://www.chesscafe.com/text/heisman06.pdf
"... To begin with, only study the main lines ... you can easily fill in the unusual lines later. ..." - GM John Nunn (2006)
"... For inexperienced players, I think the model that bases opening discussions on more or less complete games that are fully annotated, though with a main focus on the opening and early middlegame, is the ideal. ..." - FM Carsten Hansen (2010)
"... I think people tend to be afraid of the main lines. They think: ... sure, I'm going to take up (say) 5 Bg5 against the Semi-Slav, once I've got time and learned it properly. ... My advice is - don't bother. The more you learn anyway, the more you'll recognize how little you know. ... 5 Bg5 is a good move - get it on the board, get ready to fight, and see what happens.
Sure, there will come a time, whether on move two or move twenty, when your knowledge of theory runs out and you have to decide what to do on your own. ... sometimes you will leave theory first, sometimes your opponent. Nothing will stop this happening. It happens in every well-contested GM game at some point, usually a very significant point. This is a part of the game: an important part, something you have to get better at. ... to improve you have to challenge yourself; ..." - IM John Cox (2006)

ABSOLUTELY NOT!!

Memorization won't do you any good what-so-ever.  You need to actually understand what you are doing.  

I shall use the 2 examples on myself to illustrate:

French Defense:

1.e4 e6 (why are 1...e5, 1...c5, 1...c6, and 1...e6 viewed as better than other moves? Because they contest the center - the first two prevent e4 without it being traded, and the latter two contest e4 on move 2, forcing it to advance (removing control of the light squares), exchange, or be protected with risk of Black exchanging).

2.d4 d5 (Black must contest the center - 2...by, Owen's Defense, is weaker).

Now White must advance e5, exchange exd5, or protect with Nd2, Nc3, or Bd3 (popular recently).

After the strongest 3.Nc3, Black must continue to press e4 to break up the big center.  3...Nf6 directly attacks e4 again.  3...Bb4 pins the defender.  If White caves and plays e4, then the focus shifts to attacking d4 since you want to attack the base of the pawn chain, not the front.  The French also requires the understanding of pawn lovers.  The moves go on and on.

Grunfeld - I can spew out lines.  1.d4 Nf6 2.c4 g6 3.Nc3 d5 4.cxd5 (4.Nf3 Bg7 5.Qb3 dxc4 6.Qxc4) Nxd5 5.e4 Nxc3 6.bxc3 Bg7 7.Bc4 (7.Nf3 and 8.Rb1) c5 8.Ne2 Nc6 9.Be3 O-O 10.O-O Bg4 11.f3 Na5 12.Bxf7+.

Ok, what if White plays 5.Bd2?  What if White plays 10.Rc1?  Beats me!  Sure I may have a few lines memorized, but I do not understand the Grunfeld.  You deviate slightly and I am lost.

You deviate in the French, like 1.e4 e6 2.f4?!, Understanding that Black's attack is to entice e5 and then Attack d4, with the f-pawn advanced too early, White can have issues with the g1-a7 diagonal and pins on the d4 pawn.  White's e5 point is strengthened, but d4 is super weak and tactics involving pins to the king have to be watched out for.

The Queens Indian is also a commonly misunderstood opening.  1.d4 Nf6 2.c4 e6 3.Nc3, the Queens Indian cannot be played.  If you play 3...by, you do not understand the whole point.  The whole point is to prevent e4.  So against 3.Nc3, threatening e4, Black must act fast.  3...Bb4 and 3...d5 both directly prevent e4 and 3...c5 harasses d4, distracting White from e4 and weakening the central dark squares for White.

After 3.Nf3, which does nothing to promote e4, Black now has 2 moves to stop d4, and so 3...by and 4...Bb7 is possible.

I only gave the first few moves of these examples, but you need to understand WAY deeper than that!

Investing in opening books is the way to solve this problem.  The Move by Move series, the First Steps, and the Starting Out series are the places to start.  After a year or two,more in depth books on the opening are critical.  I probably own about 20 books on the French and 15 or so books on the Kings Indian Defense.

https://www.chess.com/forum/view/chess-openings/best-books-resources-to-learn-the-black-side-of-the-open-games?page=3

I would suggest taking an easy opening, where it doesn't matter what the opponent plays, therefore it will be easy to learn. You can try this opening:

https://youtu.be/23Ij7-jGehc

Having played many openings against 1. d4 over the years (KID, Benoni, Dutch, Nimzo/Bogo) and found myself somewhat uncomfortable with all of them, I recently decided to switch to the QGD. My current study material is "Play the Queen's Gambit" by Marović, which is excellent. As usual with Marović, the book uses complete games and clearly explains the ideas involved.

That said, thank you for mentioning the Sadler book, of which I was not aware. After checking it out on Amazon, I am very impressed. If my foray into the QGD becomes somewhat permanent, it will be my next opening book.

Some more recent possibilities to consider:

The Queen's Gambit Declined Move by Move

https://www.newinchess.com/media/wysiwyg/product_pdf/7743.pdf

Playing 1.d4 d5

https://www.chess.com/blog/pfren/playing-1-d5-d5-a-classical-repertoire

https://www.qualitychess.co.uk/ebooks/Playing1d4d5-excerpt.pdf

Yes, that is fantastic introductory opening book.  In terms of differences with Sadler's book (besides the openings themselves), Emms covers the open games after move 1, whereas Sadler's work starts after move 2.  Hence, Emms is mathematically dealing with a much broader task of trying to explain a much broader universe of opening possibilities in a similar number of pages. 

Sadler's scope is narrower, the QGD only, and so in roughly a similar number of pages as the Emms book, he really fleshes out the logic of the QGD lines he covers superbly.  I think it is telling that Emms, in his preface of that First Steps book, says that he intended that book to be a sequel to his other well-written work "Discovering Chess Openings" and I can agree given the ubiquity that high-level players and coaches recommend the open games for lower-level players. 

"... everyone is different, so what works for one person may likely fail with another ..." - NM Dan Heisman (2002)

https://web.archive.org/web/20140627084053/http://www.chesscafe.com/text/heisman19.pdf