The question is do you prefer an auto update for your WordPress site or not?
This is an endless debate in WordPress community.
As a web designer would I suggest an auto update to my clients?
I would not recommend it. Because it can cause some problem with automatically update the WordPress core and your plugins, or with your existing theme. Your theme or plugins may have compatibility problems. Then you may see error on the screen, rather than your site, which can be very annoying.
I would strongly recommend my clients to make manual updates to everything, in this way they can be sure that the site work without any problem, or if there is a problem, it will be minor, easy to fix.
Always make a back up the site before making any updates.
Here is the simple chart to explain what is stored in the WP website.
There are a few good plugins to do backup your database.
WordPress supports importing data in the form of posts (articles). Your written content can be import or export. Content Import scripts can be found under Tools → Import menu of your WordPress administration interface.
You can also install import / export plugins to your site. I use WordPress Importer. The plugin import posts, pages, comments, custom fields, categories, tags and more from a WordPress export file.
Keep in mind Do not forget backing up your site is not just the responsibility of the hosting provider. Your hosting provider will usually provide a backup option , but how often they do back up you still need to learn. The database needs to be backed once a week or once a month, depending upon how often and how much content you add to your site.
How will you know if there is an update? When you login your website as admin, you will see update warnings.
All you have to do; back up your files, then click on update button.