What to back up

Your priority should be to back up your most important files as well as those that are difficult to recreate. For example, ranked from most important to least important:

個人的なファイル: This may include documents, spreadsheets, email, calendar appointments, financial data, family photos, or any other personal files that you would consider irreplaceable.
個人的な設定: This includes changes you may have made to colors, backgrounds, screen resolution and mouse settings on your desktop. This also includes application preferences, such as settings for LibreOffice, your music player, and your email program. These are replaceable, but may take a while to recreate.
システム設定: Most people never change the system settings that are created during installation. If you do customize your system settings for some reason then you may wish to back up these settings.
Installed software: The software you use can normally be restored quite quickly after a serious computer problem by reinstalling it.

In general, you will want to back up files that are irreplaceable and files that require a great time investment to replace without a backup. If things are easy to replace, on the other hand, you may not want to use up disk space by having backups of them.