There are plenty of good resources out there, so there's no one best option. So, try what you can, see what jives with you, and then stick with it.
Anyway, here are the resources I used and liked:
I used this to quickly go through all the important kanji and their meanings. I neglected readings, but I think it was worth it, since now I can recognize characters more confidently, and pick up readings in context with vocabulary.
Unfortunately it's currently unavailable via Amazon, but the item listing lets you preview the book. Use that to see if you like it. Alternatively, see if you can find it at a local bookstore so you can page through it (I bought mine at Barnes & Noble), or check your local library (which may be able to order it if you ask for it). You can also use those methods to preview other books, like RTK.
KanjiStudy. It's an app for Android (and iPhone, but last I checked, that version is considerably behind). Great for quizzes and writing practice, and it supports grouping the kanji by whatever order you want, be it KKLC, RTK, Japanese grade levels, etc. $10 and super worth it (again, at least on Android), but you can try it for free to access the kana, radicals, and one "level" of Kanji for each learning order. The only think it's missing is a spaced repetition system, but that's coming eventually.
WaniKani. I like it as a convenient supplement to keep me studying kanji regularly. You can get many of the same features with an Anki deck, so it's up to you if it's worth the convenience, style, and audio samples. The mnemonics have improved, but are still way too goofy for me, but that's what I have KKLC for anyway. There's a free trial, so it's worth checking out. Plus the people running the site and the community seem cool. Also, it includes vocabulary, which is nice, and has an API to integrate with other apps, like BunPro and SatoriReader, which can add a little value.
I have no idea if it’s an efficient method or not but I use The Kodansha kanji learner’s course.
I do 16 new kanji a day and I use the anki deck for the book to keep them in my memory. Whenever I flip a card, no matter the side, I write it down. Helps me remember better. I only try to remember the main On reading for each kanji and even then I don’t force it. If I can’t memorize it I don’t try that much harder. For the readings I just read a lot of texts and when I come across a word that uses a kanji I know I don’t know the reading of, that’s how I learn the readings. Eventually you become magically able to determine the reading for words even with kanji that have a lot of different pronunciations.
Much cheaper on Amazon UK.
That said, I've found that the kanji separately really helped my Japanese studying. If nothing else, it's kept me from falling too far behind the Chinese and Taiwanese students in class...
The book I used for the kanji is The Kodansha Kanji Learner's Course by Andrew Scott Conning. Can't recommend it enough.