I think the most important thing to be concerned about when beginning a language is motivation. You have to check up on this first for yourself to see how much "motivational mileage" your brain has. Is it enough to get through the times when you feel like ripping up your grammar book?
If you've got that sorted out it doesn't really matter what order you do things because you've got to marry the whole thing, she's going to be with you every day even when you brush your teeth! So if your really serious with this girl 「日本語」 then go for it! The great thing about her is she will never drain your bank account since there are so many great Japanese resources available on the web for
free.
If you really want to try an organized approach in the beginning (just to see how long it lasts) then take about two weeks to master the kana. Now this is about the only occasion I've gotten much use from a Japanese study book (Remembering the Kana by James W. Heisig) but you can find any old website that lists the kana and then use flash cards to remember them.
Once you've got a firm base in the kana and their corresponding pronunciations then you can do anything you want as long as it keeps you motivated. Download Japanese TV programs; listen to Japanese music, podcasts, anything you can find. Every time you encounter some of the language questions will start to pop up in your head... 'well what is this masu thing they keep ending all their sentences with?' Then comes the hard part... slowly unraveling the mystery shrouding this language from your comprehension.
As soon as you feel comfortable that you're locked in, motivated, and have a very basic understanding of how the language works then start learning Kanji because the sooner you are able to take up the task the easier your work will become. Learning 2000+ kanji is a daunting task when you first start; it's even more daunting when you realize it doesn't actually enable you to read Japanese. But once you've got the first 80 or so kanji down and after staring at Japanese sentences for hours in disgust, you reach
satori 「悟り」
enlightenment. The pieces of this giant jigsaw puzzle begin to come together on the board. By now your hooked, studying grammar has become like listening to a fine elucidation by Plato and each new kanji is like deciphering an ancient Egyptian hieroglyph or perhaps a better analogy; discovering a row of chocolate in the candy store.
Now at this point you'd go brag to your friends about your Japanese ability but a little voice pops up in your head speaking in Japanese saying something like: 'always downplay your ability.'
頑張ろうね!
Resources:
http://www.japanesepod101.com
http://www.manythings.org/japanese/kana/
http://japanese.about.com/blkodarchives.htm
http://www.polarcloud.com/rikaichan/
http://wakan.manga.cz/
http://www.csse.monash.edu.au/~jwb/wwwjdic.html
http://www.guidetojapanese.org
http://www.yuukimaomi.com/blog/index.php
http://www.wadeb.com/cuecard/