You can click the cloud icon to pause the cloud sync. You'd miss out on the automatic intelligence search though.
Does the pause feature stay paused until I unpause it, even after restarts or updates? It would be nice if there were a checkbox somewhere that said "never sync".
It definitely survives restarts. We haven't had an update to test that theory fully yet, but you could put in a feature request for your Never Sync checkbox here: Lightroom CC | Photoshop Family Customer Community
I only use it on my desktop and don't want my photos uploaded without my explicit permission and decision. Should I just stay with classic
Yes, you should stay with Lightroom Classic and keep sync turned off. Lightroom Classic is designed around photos being stored on your computer, so it's what you want.
Lightroom CC uses the cloud as central storage for multiple devices, so although you could force it to not connect, that would go against how it's designed.
The answer is to stay with Classic the whole point of CC is cloud support.
If you are not interested in that level of cloud storage stick with CC Classic it still has more features than the new CC, you can add on additional Cloud Storage for those images you do want to send up, and Adobe says that it will continue to fully support and develop CC Classic.