Is there a way - with CiviCRM on WordPress - when an unauthenticated user registers for an event, it'll send an email with a link they need to click on to confirm their registratin?
If you wish them to be authenticated users, you'll probably need a wordpress plugin such as Profile Builder, to get email confirmation activated. I dont think Wordpress offers a default process to do this for new users.
In your relevant civievent template and the online registration tab, it will indicate the profile that is being used. Go to Administer/Customize data and screens/Profiles and select settings for the appropriate profile title. In the advanced settings there is a section called "WordPress user account registration option?" with an option for "Account creation required". Together with the aforementioned plugin or something similar, this should ensure that new users get an authorisation email from wordpress to register as a user.
In the civievent template online registration tab, there are settings where you can switch on "Send Confirmation Email".
Hope this helps.
You might want to consider using Caldera Form Wordpress plugin, then add the CIVICRM Caldera Form as well (https://github.com/mecachisenros/cf-civicrm). This provides a more powerful way to register various forms with CIVICRM including events. Though i have not done what you asked here on email verification as part of registration, i saw that Caldera has a free plugin with registration (Verify Email for Caldera Forms) which does what you mentioned. I think it is worth a try.