Watch anime all you want, it's bound not to be realistic at all and you will learn no relevant and/or useful japanese from it.
The above statement isn't meant to be mean, but I've been where you are, and I study japanese from a native teacher now. After more than three years of trying to learn it naturally, you just can't do that as a "westerner".
As far as anime goes. . . I only know the sci-fi fantasy stuff so. . .
Well anyways.
Hope I didn't put you down all too much, good luck with your new goal =D