Before you do anything, you need to be clear about what you are trying to achieve, as storing original images in the cloud and then using Classic "for a small catalog for printing and portfolio work" can be fraught with difficulties.
There's a simple way to do the first part of it, and that's basically to migrate the Classic catalog to the cloud via the Lightroom Desktop app. In terms of the existing assets in the cloud, if both the Desktop app and Classic are up-to-date in syncing terms, with no pending activity, then it should be safe to completely clear the contents of the cloud, knowing that they will be added back during the migration (though in all probabilty the migration function should be smart enough to deal with duplicate assets if you leave the images in the cloud first and then migrate).
But once you've migrated everything, you're faced with the challenge of that "small catalog". You cannot create a new catalog and sync to the cloud in the hopes of only downloading the few select images, it doesn't work that way. If you sync-enable a Classic catalog a full copy of the entire contents of the cloud are automatically downloded and stored locally. Not what you want!
You could export the selected images, using the "Original" format to include all edits and metadata, and them import them into your small Classic catalog which has syncing disabled. You can them work and print in Classic, but the work you do there cannot be synced back to the cloud from Classic. If you need it back in the cloud, you'd have to save metadata to the files in Classic, remove the original from the cloud, then import the saved files from the hard drive into the Lightroom Desktop app to get them back in the cloud. Plenty of scope for mistakes in that kind of a workflow, though I do believe some users are using it successfully, though obviously great care would be needed.
I guess the question is: do you want/need the originals in the cloud? You could sync your entire Classic library to the cloud as smart previews, using up none of the cloud storage allowance, and still having all the library on your mobile devices if that's of interest. Personally, I like having all my originals in the cloud, and I still also use Classic as well, but I have to jump through some hoops to maintain that "hybrid" workflow which would be unsustainable if I was a busy pro rather than a non-so-busy hobbyist.
All of your images in the Cloud!- Will you need to pay for more than the 20GB supplied with the Photography Plan ? (eg. 1TB @ US19.99/m)
Lightroom (Cloud based) only has limited organizing skills (No folders!, etc) compared to the versatile Lightroom-Classic!
If you 'Sync' a Lightroom-Classic catalog with the Cloud then it will download ALL files stored in the Cloud! (You will not need to "export a mobile file back to Lightroom classic"! It happens automatically!!)