There are a few ways to clean out your mailbox, but the most efficient option is to manually remove any superfluous emails first, then empty the trash can. Keep in mind that emails aren't truly deleted until they've been removed from the trash.
Simply right-click on the trash can and select 'Empty Folder' to empty it.
It's better to execute an archive after personally sorting through the messages. All emails older than a date you specify will be archived and placed in their own file, which will not count against your mailbox limit. You will still be able to access these emails, but it will just be a separate file. This will take care of any leftover items that you don’t want to delete but aren’t needed immediately