[Orcrist]

As for learning japanese:
Start with learning yourself kana. Just grab the kana charts of the internet and memorize them. Test yourself at realkana.com till you can remember them all then start moving on to whatever kana with romaji translation text you can get your hands on and develop some reading skills. If you have some money to spare, get the flashcards from whiterabbitpress. But it helps alot if you start out with kana, and actually start learning vocabulary in kana instead of romaji. Also, you cant teach yourself the wrong things when studying kana. Just dont start learning to write them just yet if you ever wanna be able to write them flawless (if you start learning to write the characters yourself you end up making a wrong order of strokes which will be hard to learn right after that).
Got the kana nailed? Go get yourself some grammar lessons, with every japanese sentence/word written in kana ofc. Just make sure you are learning the right grammar. I would recommend getting a decent method for this, but its gonna cost some.
What is often used alongside with the JLPT's is Japanese for Busy people. Which seems to be decent, and the method of Genki is getting alot of positive remarks from troughout the community aswell (being used on several universities aswell). So can't go really wrong with those two.

As for manga/anime, the TS is right; its not "normal" japanese they speak there. However any exposure to the japanese language is good. You will get used to the phonetics ánd it will be more easy for you when you actually start building a vocabulary. But don't use it as a learning tool, use it as a form of entertainment and the educational use of it will come along with it. If you actually start using it as an educational tool you will end up learning japanese that will be lolled at. And the advantage of anime japanese over lets say a japanese news broadcast is that in anime the characters tend to talk a little slower and pronounciate somewhat more clear (this has to be done to actually bring into some drama effects whatsoever). Someone with little exposure to the japanese language will have a really hard time making even a distinction between words spoken in a sentence by the news reporter, which is less likely to happen when that same person watches an anime.

I myself am just learning kana at the moment, but I have done alot of research in what would be the best method to actually get somewhere with a great basis. So don't take this info just for granted, do some research of yourself aswell to verify it. And keep verifying everything people are trying to tell you, if you dont have atleast 3 decent sources providing you with the same information you may be teaching yourself something wrong.