After Installing Lighroom, the essential files to copy are- The Catalog, Presets, AND YOUR IMAGES!
Lightroom, being a database type program, must have your catalog and image files, preferably in the same 'new' location as they were in the 'old' computer.
To ease the transfer the Image files should be copied keeping the exact same folder layout. If that is on an external hard-drive, then all the simpler to just plug it into the 'new' computer and open the Catalog (xxxx.LRCAT)
Relinking the image files to the catalog may be necessary and there is much advice on this available. (See link below)
Best advice I have seen is here-
Thanks - I found the Lightroom Queen article at the link and moved over the recommended files. My photos are on an external Pegasus drive, so I just had to plug it in. After copying over the Catalog, Preview, Presets - I opened up the catalog file and everything was there!