This app was mentioned in 3 comments, with an average of 1.33 upvotes
Are you specifically wanting a Kanji app? If you have an android there's the Kodansha Kanji dictionary app.
>In what order I should learn Japanese?
I recommend this order:
In my opinion if you haven't mastered kana, it doesn't make sense to go further. If you know kana just as well as Latin alphabet, things will be a thousand times easier for you.
>Which learning methods are the best?
I'm not an expert, because I've only learned kana (mastered it), but I did a thorough research and chose what I'm going to do once I'm able to study Japanese. And I'm going to use most of all textbooks, as well as some flashcards and apps.
>What websites/books to learn Japanese can you recommend?
Starting with kana, I'm not a fan of apps, but I love iKana touch from ThinkMac Software. You can learn how to draw the characters and there are four types of quizzes:
In my opinion, it's the best app for kana you can find.
As a general course I recommend GENKI textbook, for the basics. This is what I would to first. And after that I would learn from Nihongo So Matome textbooks and Shin Kanzen Masuta textbooks. You can always choose one over the other, but I want to try both of them. There are separate books for reading comprehension, listening comprehension, Kanji, vocabulary, and grammar, based on the JLPT level.
As for Kanji in general, you should definitely get The Kodansha Kanji Learner's Dictionary (KKLD). It's available in paper form as well as an app (I have both), either for Android or iOS. Japanese Kanji Flashcards from White Rabbit Press are very good too. And if I have to recommend an app, it's definitely iKanji touch by ThinkMac Software.
As for grammar, the best choice is the series of grammar dictionaries by The Japan Times. The first one is basic, the second one is intermediate, and the third one is advanced. In the first one there is Romaji, but starting with the second one there is no Romaji at all.
Unfortunately all of my recommendations are pricey (that's why I don't even know when I'll start learning Japanese), but this is the very best you can get. Good luck!
KKLD app? It's not free though.