Konnichiwa K73SK san,
The best place to start, is by enquiring from your local Japanese consulate or a Japanese embassy.
I do not know whether your country has restrictions when applying for visas, but my country has certain stringent regulations that needs to adhere to. This is because, individuals from some Asian countries (yes, I'm from an Asian country), tend to apply for a tourist visa, but ended up working illegally in Japan. That is why, for some Asian countries, to apply for a tourist visa, let alone a working/business visa, is subjected to many pre-requisites and regulations, such as, current financial status, current working company, marital status, assests and much more. This is to "convince" the Japanese authorities you're not there to do something that is not right .. if you understand where I'm going at.
You can apply for a student visa, but again, if you're not planning to study locally (as in your statement), then you'll need some form of justification for staying in Japan for that length of period. To get a job, you'll need a working permit, but again, whether is your country subjected to stringent regulations, you'll need to check with your local Japanese consulate or embassy.
As for the cost of living, it's very subjective. It all depends on where you are staying (rental in Tokyo is high), planning to eat out or cook from home and transportation, among others.
As for pets, I have not come across any of my friends bringing pets to Japan, so I'm not able to give my advise/views/comments on that. :oops:
Hope that will helps. :)