Here are a few books that I swore by when I was just beginning my study of the language:
The basic and intermediate grammar dictionaries by Makino and Tsutsui:
A Dictionary of Basic Japanese Grammar: Makino, Seiichi, Tsutsui, Michio: 8601405255785: Amazon.com: Books
A Dictionary of Intermediate Japanese Grammar: Seiichi Makino, Michio Tsutsui: 9784789007757: Amazon.com: Books
Don't be fooled by the "basic" in the title of the first one. The analysis of the grammar is very detailed, with excellent example sentences, and I think even advanced students of the language could learn a lot from both of them.
Kodansha's Furigana J-E/E-J Dictionary:
Amazon.com: Kodansha's Furigana Japanese Dictionary: Japanese-English English-Japanese (9784770024800): Masatoshi Yoshida, Yoshikatsu Nakamura: Books
This is a good basic dictionary for a beginning student, I think. It gives you the words in context with good example sentences, in authentic Japanese script (with furigana readings for all kanji, hence the title), which is very helpful. It's a good dictionary to carry you over until you build up the reading skills necessary to work with a 国語辞典 (Japanese-Japanese dictionary).
For learning kanji, I'd recommend finding a book that provides (again) lots of reading examples in context, like the "Kanji in Context" books put together by the Inter-University Center for Japanese or the Bonjinsha "Basic Kanji" books. (The latter I personally have never used, but have heard good things about):
Mr. Evan's Japanese Language Study Resource Page
If you're looking for more of an actual traditional textbook (as opposed to more reference-type works above) then I'm not sure what to recommend. The first textbook I ever used was
Yookoso!, which I don't think I could recommend with any confidence, because it always seemed lacking to me in terms of detailed grammar explanations and authentic conversational examples. There are new(er) textbooks like Genki and Nakama that I've heard good things about, but I've personally never used them -- maybe someone else here who has could offer some impressions?
I may take a lot of heat for saying this, but I still find Jorden's
Japanese: The Spoken Language to be a well-structured textbook with excellent grammar explanations (though perhaps a bit difficult to wade through if linguistics isn't your thing) and a good variety of drills and example conversations.
I know that a lot of people think Jorden is TEH EVIL for using romaji (and bizarre, non-standard "roomazi" at that!) but I've always believed that as long as you supplement JSL with materials to learn the written language, it's not really an issue. Some people make it sound like even taking one look at romaji will stunt your Japanese pronunciation terribly forever and ever, but really, out of all the textbooks I've seen, Jorden's is the only one that covers Japanese intonation and pitch accent in depth, and careful study of these (if used in conjunction with the audio materials so you actually can hear the native models before trying to reproduce the accent yourself) will go a long way towards making your Japanese sound natural to native speakers.
Also on the topic of pronunciation, I found a rather nice text called 日本語の発音教室 published by Kuroshio Shuppan, but it's entirely in Japanese so I could only recommend it to high-intermediate/advanced learners.
Anyway, I'm not sure that this is a direct answer to your question, but hopefully you'll find a helpful book or two in here.
