Mike, do you really mean a total switch, i.e. you plan on using LRCC only, and no longer use LR Classic?
If yes, it's quite simple....start LRCC and use the Catalog Migration tool (in the File menu), point to your Classic catalog and LRCC will do the rest, which effectively means importing all the current Classic images, together with the associated metadata. It will copy the existing images to the storage location specified in the LRCC preferences, and it will then proceed to upload them to the cloud.
A couple of things to note:
1. Get your Classic catalog into a clean state first, i.e. no missing images. Any missing images cannot be migrated.
2. Make sure you have sufficient available disk space in the specified LRCC location, as effectively your existing image library is initially duplicated (so yes, when all is done, your existing Classic-cataloged images are still on your hard drive).
3. Depending on your LRCC preferences, that local copy of the images that LRCC initially creates will remain (if you have selected to "Store a copy of all originals"), or will gradually be removed (if that preference is unchecked).
But if you are planning to continue to use Classic and LRCC in a combined hybrid workflow, the Catalog Migration tool is NOT the right way to do this.