A couple of questions

1. I think it's more of wanting to preserve it because it holds significance, rather than actually wanting to watch it per se.

2. I agree that the definition of "well known" versus "lesser known" media is very iffy, even because what the "general public" knows might vary depending on where they are from or what kind of media they were allowed/able to consume throughout their life. Personally speaking, I think some of the things which are pretty much always regarded as "lesser known media" are local commercials, indie or local productions (e.g. someone from your hometown made a short film that was put on youtube for a while and it is unlikely that people outside of that social circle ever heard of it), or internet content that wasn't hosted on big websites.

Unfortunately, the concept of Lost Media tends to be very English-centric. I'm from Brazil, and most of the content I consumed growing up was dubbed versions of shows that aired elsewhere, and several of those dubs are nearly impossible to find. When it comes to local shows, advertisements, or even TV channel bumpers, the search is pretty much futile.

With that said, I suppose media that is "relatively known amongst the general public" can be considered anything with international value, either owned by a big distributor or hosted in a big platform.