Be aware that there's really no annual immigration intake into Japan. It's not like Australia, where I'm from, which takes in 150,000+ migrants a year. You can't just apply to come live in Japan because you think it's such an awesome place. You'll need to get a sponsored work visa to stay here any length of time or marry a Japanese person.
Even if you speak/read fluent Japanese don't expect to be able to just get a job in Japan with a Japanese company. Not only will you need the absolute minimum of a university/college degree (and depending on the position possibly many years of previous experience) but for a Japanese company to employ you you'll need to have pretty specialist skills that can't readily be found in Japan. Otherwise why would a Japanese company go to the trouble of organising a sponsored visa for you and how could they justify it to immigration?
This is why so many people get their foot in the door through english teaching. This is obviously a specialist skill that you (if your native language is english) have an advantage over the locals. Once you've got a sponsored working visa it's then reasonably easy to continue to stay here and move around between jobs. Once you have the visa you'll find many more opportunities open up as there are plenty of jobs only available to people in country with a valid visa. If you have the Japanese language skills then the range expands greatly depending on your qualifications and experience.
That's if you want to work for a Japanese company. There are of course a lot of foreign companies with branches in Japan and if you work for one of those companies you can try your hardest to get stationed here for a time. There are also quite a lot of foreigner owned companies operating out of Japan and they may mostly cater to foreigners already here or from elsewhere. These companies may not require you have Japanese language skills barely at all. And if they are providing a service or product mostly to foreigners then they may have an easier time convincing immigration that they need for instance a native english speaker to fill a position. Where I live and work there are many foreigner owned businesses involved in property development, management and sales as well as a number of tour companies. And the companies will sponsor visas for certain positions.
Still on the whole I reckon unless you've got some pretty cool skills that aren't readily found in Japan (just a heads up, there's no shortage of local anime/manga artists
) then your best bet is to try and get in through a major eikaiwa or a program like JET. Once you're in then you'll have the opportunity to start looking elsewhere if you want to move onto something different.