I use Japanese for Everyone. It's an excellent text, but has some flaws. It's very compact (this 1 book = 2 Genki books = 3 JBP books); vocabulary is spread all over the place, usually listed separately but not always; the index is romaji to English only, no English to Japanese; there is some amount of romaji in the first 6 chapters. I'm committed to this book because I'm almost halfway through. If I had to do it over again, I would go with Genki. Genki is very similar, but has fixed all but the romaji issues listed above.
JBP has some good points. The kana version has no romaji in it; it moves at a very slow, comfortable pace. Unfortunately, there are many bad points. Plain form was not introduced in the first book; examples are favored over grammar rules; vocabulary is quite business-oriented; etc.
Minna no nihongo may be great for non-native English speakers; it teaches you Japanese in Japanese. I only saw the second book, but it uses a lot of kanji, usually with hurigana. It has a lot of group exercises, which aren't too useful for self-learners. Also, I'm pretty sure that even though I was halfway through the second book, plain form had not yet been taught; all the examples I'd seen were in polite form.
Japanese the Spoken Language was all romaji, so I didn't give it a fair try, although I hear it has very good grammar explanations, and a good audio program.
Everybody learns differently, so there is probably a "best text" for you that might not be the best for me. But here is what I like.
1. Early introduction of plain form. If you want to be able to listen, it's crucial to learn this early, and learn it well. Japanese learn this first, and think in it, so it's pretty important.
2. English explanations of grammar. Minna no nihongo taught me that learning Japanese in Japanese doesn't work for me. If there weren't any good texts in my mother tongue, I would probably use it, but fortunately this is not the case. To go a step further, the explanations should be written by someone that has excellent knowledge of both languages. Some texts seem like they were written in Japanese, and later translated, giving confusing grammar explanations.
3. Little, if any, romaji. I'm a little divided on this actually - I now regret giving away my Japanese the Spoken Language a little. Maybe I could have learned basic grammar quickly with that text, then gone cold turkey off of romaji. This is how some people learn. I think the main reason romaji is feared is that people get so comfortable with it they don't have the will power to change over to kana/kanji. Seeing a low rate in literacy, most teachers now recommend against romaji. But maybe I'm one of the few who could have pulled it off. I'll never know, because I went down the other path. So no romaji for me.
4. Good audio. Unfortunately, except for Japanese the Spoken Language, good audio doesn't exist for texts. There is usually some audio, but it's typically just the dialogs, sometimes a handful of listening exercises. After studying and drilling grammar in flashcards (supermemo), I really need all the exercises in audio form (I make my own). Think of it this way: I'm a self-learner, and it's a big step to go from flashcards to conversation. Baby steps have been shown to be the most efficient way to learn (Stephen Krashen, What about Bob, etc.). Audio is a step between flashcards and conversation - it makes my responses lightning fast.
5. Good organization, indices, pictures, interesting examples, etc, etc.
Edited: 2006-09-29, 11:01 am
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