Syndication is also called reruns, when the show is rerun out of order on TV at a standard Timeslot. Like for me TNG was on every night at 7pm M-F. It was shown in random order as far as I know with I believe them skipping less popular episodes, I honestly never noticed if they did hits for a bit then did a rerun through it or what.
The first season of TNG is considered weak as a heads up, similar for DS9 though DS9 has some bangers in S1, TNG is mostly weak. That said if you like it, you’ll LOVE the rest.
SNW is fantastic and I really recommend it, it is certainly New Trek but it’s a MUCH better successor to the legacy than Discovery.
Admiral April and Admiral Forrest are both solid options.
I think April did a really solid job of showing what a great but imperfect leader looks like in Ad Astra per Aspera.
Forrest was supportive and helpful. Willing to bend the rules to support his people rather than vice versa.