Any database changes WP itself needs are performed automatically. On first load after core update you will get (if required) special page that will say that database update is required and perform that update. No actions required from you really.
Changes and updates to database by plugins can vary and not many plugins actually need or perform them. If you perform plugin updates manually it’s recommended to disable them, updating plugins inside WordPress will do that for you automatically if I remember right.
All data is supposed to be retained on updates. It is still recommended to make backup before updates (I usually skip it, but only because I have solid scheduled backups anyway).
Overall if updating grossly outdated installation I’d go with following:
- Perform full backup of both files and database.
- Deactivate all plugins.
- Update WordPress core, let it run database update.
- Update all plugins.
- Re-activate plugins one by one.
If there are some old plugins, critical to site’s operation, it might be better to first copy site to local WP installation and test both upgrade process and operation of plugins with new WP version.