It's better to have a lossy copy than no copy.

What are you trying to archive? Is it the words the person is saying, or the arrangement of his freckles? Even the lowest video quality is sufficient to convey all of the information content of most videos. Sometimes the audio alone is sufficient.

The file size difference between the 360p and 4k versions of the video can be 95% or more. That is to say you can archive twenty times more videos. I wouldn't recommend going below 360p. At 360p expect to store around 1-2 MB per minute.