One of the easiest options for avoiding ads – and gaining the ability to “save” videos for playback later – is a subscription to YouTube Premium. While not cheap, it does eliminate the annoying ads. Something to consider if you spend a fair amount of time on YouTube.
YouTube Premium does allow you to download videos, but only for playback with the YouTube app on a smart phone or tablet. No downloading to PC’s. See How do I share a YouTube video in Zoom? on this page to get the video from your phone out to your students.