yeah, that's the issue isn't it - nearly a thousand episodes!

you could go for star trek: prodigy, an animated kids show which was explicitly created to be an ideal starting point for the series (plus due to Licensing Shenanigans it's on a completely different set of streaming services from the other ones, so it's likely either the easiest or hardest for you to access)

you could go in release order, though be warned that the original series, while ahead of its time in some ways, is very of its time in others - including some misogyny

or you could just pick a show or movie that sounds interesting, and start there. all of the shows except discovery, picard, and prodigy are mostly episodic, so you could even pick a random episode that sounds interesting. just going by your interests you seem like you'd be into star trek: discovery, because of its complex main character and modern production values