What is the best way to go about transferring my Catalog to a new computer, and new version of Photo

The best way is to create a full backup of the 2018 catalog on your old computer and restore it on your new computer using Elements 2021.  I recommend that before you backup the catalog, make sure there are no missing files.  (Go to Find>All Missing Files and either reconnect or delete from the catalog any missing files.)  Also, in File>Manage Catalogs, Repair and Optimize the catalog.  (Complete these processes even if the Repair says there are no errors.)

Given the size of your old catalog, you will need a large external drive to save the backup. 

When you restore the catalog to the new computer, the program will convert the catalog to an updated format.  This may take a long time.  Be patient, even if the program seems to be non-responsive.

One other point.  I think I would recommend restoring the media files to the original folder structure.  Since the system folder names are different between Win 8 and Win 10, you may end up with a little bit of an unusual folder structure that includes a folder named Pictures as well as My Pictures or My Photos or whatever it was called in Win 8.

Here are a couple of HelpX  articles that may be of help to you:

Backup or Restore Catalogs

Troubleshoot Catalog Issues