I'm a bad shill for Picard, I am about as down on the whole thing equally. Ultimately I just don't need to revisit old heroes, ever. I hate this future of all our heroes being basically watching our dads grow old and sad and frail. But yeah, people like S3 more because it's more of a fanservice-y thing than trying to tell the adventures of old Picard by himself, so if that sounds appealing to you go for it.

As for Discovery... yeah, absolutely, skip Season 1. Season 2 is the one that ties into SNW, so if you watched that, you can jump in right there and it's almost a stand-alone show that feels a lot more consistent with SNW and a lot less consistent with Season 1. I'd still go back and watch S1 later if you enjoy the rest of it, but skipping that is absolutely a valid watch order if you don't want to do the "trudge through the bad first season" thing of most Star Trek shows. I actually quite like seasons 2 and 4 specially. I'd rank them above all of Picard and just behind SNW, as far as nuTrek is concerned, and I'd rather watch those than most of Voyager and DS9, if I'm being honest.

The TOS Kirk thing is... interesting. I mean, you're not wrong, Kirk was supposed to be just an all-around good guy Mary Sue who's always great and right. It's just that 60s Trek take on that turns out to be almost comedically horny and rash, especially as parsed by Shatner's acting choices, especially when you retroactively compare it to TNG, which, let's face it, is the de facto standard people have for what default Trek is. I think SNW's Kirk splits the difference just fine... but he feels like an entirely different character. I can almost see Pine's Kirk growing into Shatner's more than I can Paul Wesley's. But from the perspective you present? Yeah, they paint him as being more aggressive than Pike, for better or worse, but also mostly just smart and nice rather than a horny hothead. Definitely not doing Shatner, though, and less iconic than either of the other takes, I'd say. Which is fine, it's Anson Mount's show anyway. If anything I'd have liked less Kirk in the two seasons they've done so far. Hell, I'd have taken that cast in a standalone show rather than a prequel.

Shout out to Martin Quinn's Scotty, though. He got like two episodes so far and already he's the one cast member who I can see as the same character from TOS. The others are fine, they're just playing their own take on the character's premise, as opposed to the same character from the original.