ALWAYS take a database backup and file backup of the website before you update. If something does go wrong you can revert.
If you want to avoid as much interruption as possible, set up a local or development copy of the site and perform the update there. When you are done, back up your development server and launch that on the live site again.
If 30 minutes of downtime won’t kill you, it might be quicker to update directly. But if something does go wrong, your website will be offline until you restore the backup.
If you do not have many 3rd party plugins and your theme is recently updated, it should go pretty smoothly. The older your theme/plugins, and the more you have, the more likely you will experience issues.
WordPress does a pretty good job at providing backwards compatibility, but plugin/theme authors are a different story.