What Grammar Girl fails to mention is the difference between mechanics and style.

Prepositions in most compositions do not need need to be placed at the end of sentences. Although questions are asked in in compositions, especially at the college level, they are usually broad and never questions like "what did you step on?" This is why your JHS and HS English teachers (ME) hammer home the idea. Rules are made to be broken, but you need to understand where and when you can break them by learning mechanics before you attempt style.

In Texas we use learnt (more often burnt as an example of ed vs. t for past tense conjugations).

I recommend you learn Japanese grammar first, THEN learn vocab to plug in.

But you have to know hiragana pretty well and a LOT of words first..

No, you don't. Chinese is written entirely with Kanji. In fact 漢字 means "Chinese Character." Not only are there people who do study 漢字 without knowing hiragana, there are people who use a method of study where they don't even learn kun-yomi or on-yomi, but just ei-yomi: that is, they do not learn the Japanese native sound nor the sound based on the Chinese reading, but just the English meaning.

Without hiragana though, you will unable to understand conjugations, particles, as well as many common or less common words that are usually written such, even if they do have kanji. I do not recommend learning kanji by itself, nor do I recommend any regimen of Japanese language usage without kanji. The best is to study them together, practicing handwriting (shuji) by actually writing entire sentences, using kanji as needed for nouns or verb stems.

I never made a focused effort to study grammar in the beginning. I'm still not very advanced but feel that I've made good progress with my listening and speaking ability... So bearing that in mind...

What I would say is that you might want to learn a bunch of common words first, then get as much exposure to the language as you can. If you have trouble with understanding something, then look it up.

You will eventually begin to get a feel for the grammar. I'm at this point now and am actually able to hold decent casual conversations unlike a lot of Japanese students who only study Kanji/Kana and reading/writing.

My idea was always to get to the most rewarding aspect of Japanese (which was conversation for myself anyway) as fast as I could and then round-out the edges after that.

At that point, you should probably learn the grammar a little more formally so that it all makes better sense to you-- that's what I'm doing now along with my Kanji studies.

I know some people on this forum will wince at my method, but it's worked well for me so far :)

Tsuwabuki, to quote Winston Churchill,

"People telling me I can't end sentences with prepositions is something up with which I will not put."

The "stylistic" prohibition on ending sentences with prepositions was made by silly grammar teachers importing rules from Latin into English in the early 1900s, if I've got the era correct.

Nonetheless, it is true that ending sentences with prepositions separates formal writing from informal in the minds of many people who matter. Thus, it is useful to obey the rule if you want to impress with your writing in formal settings despite the fact that it's a stupid rule that only idiots adhere to all the time.

And to get back on topic, I personally think you can't just focus on one thing (for too long) at the exclusion of other aspects of language learning.

But if you must, I'd say that you need to focus on a base level of maybe 100 nouns and verbs, and then you move on to some basic grammar (conjugating, changing mood, and a few auxiliary verbs and such). Then from there you need to learn more words. After a while, you'd better have started learning kanji, becase you're going to hit a point where you will learn words more efficiently if you know 1200+ kanji for this reason: Eventually, learning new Japanese words based on kanji will explode your vocabulary like learning dis-, un-, -phobia, -philia, circum-, -scope, -phone, etc. in English explodes your vocabulary.