This can be done in Mendix. However, I would start out with the Mendix academy to get the basics down and then go into developing your new application.
Getting started link - https://gettingstarted.mendixcloud.com/link/home
When you are starting the new application, creating a new user should be straight forward. I would take a look at the deeplink module for the confirmation link.
Here is a link to the Deep link module https://appstore.home.mendix.com/link/app/43/Mendix/Deep-link-module
The forgot password module has a separate workflow for people to sign up/receive an email confirmation.
Here is the link
Hope this helps!
If your question is how best to create a login-module with an email-confirmation: get some App from the appstore.
Login form, SMTP Email module and connect the dots.