Honestly, I grew up watching the original series and it was extremely formative. I can’t say that I’d never have become a scientist without it, but it did help shape my concept of myself and the way I relate to the world, and how I’d like the world to be. In fact, when next generation launched, I originally didn’t like it because I was such a fan of TOS.
However, looking at it objectively, I think that TOS holds mostly nostalgia value. I wouldn’t recommend starting there unless you have a thing for campy TV and mid century modern design themes. If you’re interested in seeing what all the fuss is about, I’d start with the second or third season of TNG or one of the later series like DS9. TNG takes about a season or two before the writers and actors start to figure it out.
If you’re really more modern-oriented, you could start with the JJ Abrams movies, which are modern action movies in the ST universe.
The main thing is this: you can start pretty much anywhere. There will be backstories or call backs that might slip past you or inside jokes that you miss, but it’s more important imo to get on board with the franchise by starting with the stuff you find enjoyable, rather than getting turned off by elements that are dated or don’t resonate. Once you have that context, you can move back and forth between all the series and movies and enjoy them more.
Think of it like Discworld. It’s a series of novels written such that you can jump in anywhere and read them forward, backward, or sideways. It’s not like Lord of the Rings where you really can’t just start with the last book because there’s a single story being told in multiple parts.