[Nyororin]

I started with Hiragana, then to Katakana, and after that increased vocabulary while learning more grammar, etc. But at that point I was in Japan, so really I could probably have skipped learning those before coming over here.
Kanji, in my opinion, should come last, and romaji should never even come into the picture.

If you try to learn Kanji earlier, before you really know what the ones you are learning mean, it seems like a waste. It`s like learning to spell long and complicated words which you don`t even know the meaning of. You forget them very quickly if you`re not at the level where you actually use and understand them.

If at all possible - especially if you`re learning from a book - you should try to learn the Hiragana first and use a book with all the Japanese written IN Japanese. Why? Because Hiragana are always ALWAYS pronounced exactly the same. With romaji you have all these possibilities. Even if you know how something is supposed to be pronounced, your mind will want to read the romaji in a more familiar way. You`ll be left with screwy pronunciation.