To add to Yubi's answer, it is important to note that Japan doesn't allow its citizens to have other country's passports. So when you receive Japanese citizenship, you are required to abandon your first citizenship. But I am not sure how strict they are with enforcing this rule. I know about cases where people kept second citizenship along with the Japanese.

Correct. Japan's goal is to not allow dual citizenship, but that is not so practical since some countries do not have a way to renounce citizenship. So, the practiced rule is to make using a passport from a different country illegal. The kids can have dual citizenship until they are 20.

Becoming a permanent resident is much easier than it used to be. The immigration bureau now has a points scheme that gives priority to certain professions, and it is publicly available on their web site.

For a person who does not benefit from the points scheme, Japanese citizenship is easier to get than the PR status. This is handled by the Law Offices (Houmukyoku), so please contact the office in your area for further details.

The shortest path for both is becoming a spouse of a Japanese citizen. Three years after marriage, you can apply.

Unless you have had problems with visa etc., both these can be applied for without the help of lawyers. An immigration lawyer will give you free advice once, but following up will cost quite a bit.