"What textbook should I use?"
"Genki" and "Minna no Nihongo" are the most popular book series because they are
pretty good. Because they are so popular, you can get the answer to just about
any line you have a question about by googling and it will already have been answered.
Genki is heavily preferred by native English speakers.
Minna no Nihongo has its "Translation and Grammatical Notes" volume translated
into a number of other languages, and is also preferred by students who want
to learn Japanese in Japanese as much as possible.
A Dictionary of Basic Japanese Grammar is a good companion to any textbook, or even the whole Basic/Intermediate/Advanced set.
"How can I learn Japanese for free?"
Tae Kim and Imabi are effectively textbook replacements, at least as far as
providing grammar lessons. They lack the extent of dialogues and exercises in
typical textbooks, so you will need to find additional practice elsewhere.
Erin's Challenge and NHK lessons teach lessons with audio.
They are not IMO enough to learn from by themselves, but you should have some exposure to the spoken language.
Anki and Memrise both replace flashcards, and are general purpose.
Koohii is a special-purpose flashcard site learning Kanji the RTK way.
Dictionaries