(oh yeah, and if you don't know what are katakana, hiragana and kanji, or what they look like, I suggest you go read this post -I know, shameless plug :P)

Right, so about what to learn and when to learn it: all the people who recommended not to rely on rômaji (romanized alphabet) too much are right, Shibori, and that for two reasons. One, very obvious, is that Japanese themselves make a very limited use of the rômaji, and they certainly never write full texts with that script. So unless one is solely interested in learning how to speak (and even then, I wouldn't recommend it), you cannot rely on rômaji alone.

There's another reason: there are a lot of homophones in Japanese, some with close meanings to boot, so the only way to be perfectly clear when writing is using the kanji; rômaji only would be far too confusing.

About the kana (term used for katakana+hiragana)/kanji dilemna: while you don't write full texts in rômaji in daily life, but it is possible in theory (actually, some books teaching Japanese do that), it is impossible to write texts in kanji alone in Japanese. Period. All the particles that indicate the structure of a sentence, the verbs and adjectives endings as well as some nouns can only be written in kana, 99.99% of the time in hiragana. Foreign words and names cannot be written in kanji either (except Chinese words) -they are also usually written in katakana.

Besides, all the books that I've studied with either introduced kana first or supposed you knew them already and started teaching kanji right away. So you won't find any material that's teaching you kanji in context without requiring that you know your kana. The only way to do that would be to learn kanji from a list alone, but you won't be able to understand them in context because you won't understand the structure without the kana. On the other hand, you can find texts written in hiragana alone, and kanji are slowly introduced (this is how they actually learn in Japanese schools).

Moreover, one more thing: if you know katakana already, you'll have no trouble learning hiragana; it's almost the same! It's the same syllables, only written a little differently, and some actually look the same. So don't worry, Shibori, learning them will take you even less time than learning katakana. ^-^

Soooo, to sum it up, I'd recommend you to learn scripts in that order:

-rômaji (because you have to at the very beginning), replaced as quickly as possible by
-hiragana
-katakana
-kanji

Although you can learn katakana first. It can be interesting because since katakana are usually used to transliterate foreign words, often borrowed from English, once you can read them, you can understand full words by guessing at the English origin. This is why you can read, and understand, such things as menus, even though katakana are used very little compared to hiragana or kanji in books, be them fiction or non-fiction. They are used a lot in mangas though, for several reasons (but I won't start here, this post is long enough already *g*)