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
