How do I migrate from a site using a core version to another one using the same version? I like to change the web-hosting provider. I want to remove un-necassary and useless stuff (e.g. modules, content types that aren't used from the site).

I have no idea how to do this. Is there a module for migrating only stuff which is in use? The migration modules I found only consider migration from previous versions to Drupal 8, not from Drupal 8 to Drupal 8.
Why don't you just uninstall those modules and remove the configuration you no longer need?

Migration is a complicated task that requires a lot of work.

And to switch the webhost, you just need to copy the files and database, no need to mix those two things together. Clean up your site first and then switch the host. Otherwise you'll never be sure if a problem is caused by the host change or changed configuration