Folders required to download when moving a Craft 3 installation to another server? If I'm downloading a Craft 3 website one server in readiness to deploy onto a new server, which folders should I download aside from?:

/templates
/web

Also, do I need to redownload the 'cpresources' folder again inside the /web directory if I already have a local copy of Craft CMS installed?
You'll need to take:

/config
/modules (if there are any custom modules, but no harm in taking it anyway)
/web
/storage/rebrand (if you have rebranded the control panel)
/templates
/translations (if you have added any static translations)
/vendor (unless you plan to run composer install on the new server)
composer.json
composer.lock
craft (CLI)

You can generally discard the whole contents of storage and cpresources as they'll get automatically recreated, unless you have put anything in storage/rebrand. However, you'll still need a storage directory, even if it's empty.