I really recommend the Japanese For Busy People books, I learned tons from them quickly. They start off very basic (obviously), but they explain the grammar in a really good way, and progress into more advanced topics as you go along. Make sure to get the kana versions, not romaji!

For learning Kanji, the most efficient option I've found is Remembering the Kanji by James Heisig. It's a bit of a long-term investment, in that it takes a while for them to really pay off (you don't learn the readings/sounds until book two, the first one is completely focused on the meaning and writing of the characters), but in the long run I think it's a much better option than for example the books trying to teach you the characters by showing you their similarity to the things the represent.