[Sangetsu]

The papers you will need from the US are proof that you are not already married to someone your home country. These are pretty easy to get.

Getting married in Japan is also easy, and can be done in a few minutes at the city office. Simply fill out the papers, and get them stamped, and you are married. It would be better to get married in Japan than in America.

But getting a visa is not necessarily so easy. Since your wife is a permanent resident, you can qualify for a spouse visa, but, she has to sponsor you, meaning that her income will have be be sufficient to support the both of you. If she's working part-time, you probably won't be able to get a spouse visa. If she has family in Japan, they may able to sponsor you, so long as they meet the income requirements. Otherwise, you'll have to go the typical route of getting a regular work visa.