Per the 出入国在留管理庁 guidelines and document list: resident and national tax certificates, pension and health insurance records, and on-time payment rules to check.
Resident tax based on your Jan 1 address and prior-year income, collection methods, who files a tax return and when, deductions for relatives abroad, 納税管理人.
Certificates most used for 在留期間更新 and 永住申請: 住民税 and 国税 certificates, 住民票の写し, pension and health insurance records, 源泉徴収票, 在職証明書: where, how, cost, when.
Procedures after marrying in Japan: 婚姻届 and the 婚姻要件具備証明書, the 世帯変更届 and 在留カード記載事項変更届出 within 14 days, dependent status in the spouse's health insurance and 国民年金 Category 3, whether a 在留資格 change is needed, and the 配偶者控除.
Procedures after leaving a job: the 所属機関に関する届出 within 14 days, the rule on cancellation after 3 consecutive months without activity, 任意継続 or 国民健康保険, 国民年金 Category 1 and the 特例免除, 雇用保険 基本手当, and 住民税 and 還付申告.
Procedures when you decide to leave Japan: 再入国許可 and loss of 在留資格, returning the 在留カード, 転出届, withdrawing from 国民健康保険, 脱退一時金 (claim within 2 years), and 納税管理人 and 準確定申告 for 住民税 and income tax.