There are so many resources out there but if you are looking for one book to get you started, Japanese For Busy People 1 is it! All the grammar points will be understood after using all three books in the series. If you are not going to buy audio tapes with this book, go to www.ajalt.org, which is the official site of the Association For Japanese Language Teaching. There are lots of audio resources there for beginners, intermediate and advanced learners. After finishing Book 1, the learner will be able to introduce themselves, shop, tell the time, express preferences, etc. It also offers quizzes to test your level.
However, one negative is the lack of vocabulary. The learner has to go online and lookup news articles. Go to http://184.108.40.206/~jems/hosokyoku/bangumi.html for articles with audio and fill in the blank quizzes.
Critics say this book tells you to memorize verb forms and adjectives but the patterns will be very obvious. As long as you are willing to put in the effort, this book will teach you everything you need to know to start.