Strange New Worlds is a great starting point. SNW is set in the 5 year mission before Kirk’s 5 year mission on the enterprise. There are some arcs that you might not get but it’s not necessary to know what the episode is about because it is episodic. I watched the corresponding TOS / Discovery episodes with Captain Pike after I watched the SNW episodes to fill in the parts that I really didn’t get but here is a list of the episodes I watched.
The Menagerie Part 1 and 2 (TOS) -> Through the Valley of Shadows (DIS) -> A quality of Mercy (SNW) -> Balance of Terror (TOS)
Picard season 3 is an absolute must if you watched next gen / DS9. For the whole season to make sense you’ll probably want to watch the last 2 seasons of DS9. If you watch the last 2 episodes of picard season 3, watch TNG’s best of both worlds part 1 & 2, All good things… (the series finale), and Voyager’s Endgame (the series finale) it’ll make more sense.
the last 2 seasons of DS9 is very political and heavy but many people say it’s the best trek - however now SNW is getting close to taking the title.