It depends on your skill level; using a tool such as phpMyAdmin as John pointed out is probably the best way to go if you have limited skills. Plesk has an export dump but it will add statements that will get in the way of using phpMyAdmin to import. Here is the other thing, if you have a large database, then phpMyAdmin may not be able to import it; depends on the settings in php.ini on post size and file upload size; plus, there is a config setting for phpMyAdmin that may limit how long the import executes. There is a utility I have used to import large databases and that is big dump: https://www.ozerov.de/bigdump/ However, you do have to export the database in a proper way to use big dump.
Backing up the site files may be a long time operation, especially if you have a lot of photos and videos on your site. cPanel has a back up utility as well as Plesk. You will want to archive the site files to make it easier to download; I think most control panels have compression backup in place using zip. If you want a copy on your local computer, then archive the site and then use a ftp programme to download that archive.
If you want a local copy for safety reasons, then archive and download. However, if you are wanting to move to a new server, then a server to server transfer is the better way to go.