If you want to see icons for the internal SSD, and external drives, on the Desktop, go into Finder / Preferences… and check off the appropriate boxes under the General tab.
I would recommend storing your files somewhere under your user directory. E.g., if jhsteele is the short name of your user account, your user directory will be the jhsteele folder within the top-level Users folder. If you open a Finder window, many (though not all) of the locations under Favorites will be shortcuts to subdirectories of your user directory, and the shortcut for your user directory itself will be marked with a little house ("home") icon.
The Pictures folder within your user directory seems like a likely place for Lightroom to place its catalog folder.
Adobe's recommendations are to keep the catalog file and preview files on a fast drive, such as your internal SSD. However, if you have a large enough photo library that you are in danger of running out of internal storage space, you can move full-size photos onto an external hard drive.
Adobe Support – Optimize [Lightroom Classic] performance
https://helpx.adobe.com/lightroom-classic/kb/optimize-performance-lightroom.html
If you're using Lightroom Classic and you want to move photos to an external drive, it's good to do this from inside Lightroom Classic itself, rather than from the Finder. That way, Lightroom Classic knows where you moved them…
https://helpx.adobe.com/lightroom-classic/help/photos.html