I'd like to let the user pick how many items are gonna be displayed on the page. Therefore, I need to display a field with a select or something.
Is there a way to make that directly through the UI, not with coding?
Yes, you can do that with Views.
In the pager settings for the View, select to expose the number of items to the user.
Make sure the textfield with available items per page options includes the default number of items per page.