'Lightroom CC' is an old name that is no longer in use. There are two versions currently. Lightroom Classic is the latest version of the Lightroom you know and use right now. If you upgrade to that version, you can simply open your old catalog, let Lightroom Classic upgrade it and continue from there. Lightroom Classic comes in the 'Photography Plan', which also includes Photoshop.
Lightroom (desktop) is a new application that stores the original images in the cloud. It's possible to 'migrate' an old Lightroom catalog, but not as old as your catalog. You would still have to upgrade your catalog with Lightroom Classic, but in that case you could install a trial version of Lightroom Classic just to do this upgrade, and then take the 'Lightroom Plan'.
There is no Lightroom "CC". There is Lightroom Classic and there is Lightroom. Lightroom Classic works much like the Lightroom 4 you have been using in that it utilizes a local catalog and stores images locally on your computer hard drive. Lightroom, on the other hand, stores images in the cloud and (optionally) a backup copy on your hard drive.
If you are choosing to upgrade to Lightroom Classic then when you install the program it will find the catalog you have been using and prompt you to upgrade it. The upgrade process is seamless and will create a new copy of your existing catalog. When the upgrade process is complete Lightroom Classic will start and you will find yourself right we left off previously.
If you are choosing to convert to Lightroom, the cloud-based version, then it will be necessary for you to install the trial version of Lightroom Classic long enough to allow it to create the upgraded copy of the catalog because that will have to be done in order for the migration process to Lightroom. Take note that only one catalog can be migrated, so if you have multiple catalogs you should probably combine them before you go through the migration process.