Genki textbooks are highly recommended for beginner learners. Its structure is easy to understand, with plenty of examples and explanations in English to help with comprehension of the content. The workbook also includes writing exercises and listening practice as well, which is highly recommended that you try out in order to bolster what you have learned.
In addition, instead of learning -masu form at the beginning, the Genki textbooks teach via the dictionary forms. While this might mean a slightly steeper learning curve at the beginning, it is more helpful in the long term as verb and adjective conjugations are easier to understand using this model.
In the beginning of every chapter, there is also a small conversation with new vocabulary and grammar that will be introduced in the chapter. These examples are useful to relate how the new grammar and vocabulary can be used in real life situations.
Finally, as an easter egg, if you actually follow through the entire series, you will realize that when you put all the conversations together, it’s actually mini story! (I shall not spoil it for you guys!)
If you already have some foundation in basic Japanese, you can start off with straight with book 2 of the Genki textbook series. The entire Genki series covers the content required for JLPT N4, and some parts of JLPT N3 as well.
In order to prepare for JLPT N3, it is required that you understand the difference between certain similar grammar structures. This grammar book by Unicom has a pretty comprehensive list of various grammar structures with accompanying descriptions and explanations. In the link above, you can actually see a sample of books’ contents as well to has a grasp of its approach in teaching.
As this is more of a reference book rather than a textbook, its learning curve is not as gentle as that of the Genki textbooks, and hence, it is highly recommended that you also do have a fairly good proficiency in reading Japanese before you start on this book.
Another series which is highly recommended is the Nihongo Sou Matome series. The vocabulary is listed according to categories (e.g. words associated with opening a bank account, words associated with renting an apartment), so this topical approach is definitely useful and helps to brush up on vocabulary.
For the two series mentioned earlier, it is best if you use them from N3 level and above; N4 and N5 levels of these reference books are not as structured as the Genki textbook and might get quite confusing.
For conversational Japanese, the shadowing textbooks are highly recommended. There are 2 books in this series, which use examples which you may often find yourself in real life situations (e.g. getting lost in a station, making reservations etc.). By listening to the audio CD, it is also a good practice to get your intonations and pronunciations correct, as well as getting used to native Japanese speed of speech.