[MENTION=70954]Smear-Gel[/MENTION], I get what you mean. A lot of people and naysayers (like those who hate modern Trek) have been saying that the references and in-jokes make 'Lower Decks' bad for newcomers but I cannot see how it would shut out so many at all. Sure, fans and those who know a decent bit about the franchise will get more of the references, but it still is a nice and entertaining show that doesn't really require any previous knowledge (I rather think a series like 'Picard' does require some knowledge due to plot points and characters being more tied to previous shows, but that one still works as a standalone too. I'd say it's my least favorite of the series' though).
And regarding the thought of Mariner and Freeman having been around on the Enterprise-D, I would say it is a possiblity Freeman has been stationed there at some point during the TNG series but I think Mariner is a bit too young for having too (but I guess during the later two TNG movies she could have been on there, at least as visitor). I think that there is a possibility that any character connections with the Enterprise could be touched upon in season 2 with Boimler on the USS Titan with Riker & Troi (at least in passing dialogue).
Anyhow, back on the live-action shows, you said you're watching TNG. I do think that is a good starting point when it comes to the older shows, even if the first couple of seasons are pretty rough, especially the first one (I watched the movies first, with 'Star Trek Into Darkness' sorta being my gateway to the franchise before seeing the classic films, and then The Original Series, which I stuck to for a few years before going to TNG, then Deep Space Nine, Voyager, Enterprise & naturally Discovery inbetween and also the 1970's Animated Series).
How far have you gotten and what do you think so far, overall?