I don't know about "getting into" consciously. For me it was just on TV when I was a kid and there were just 3 TV channels. That & Doctor Who started my lifelong love of science fiction. Thanks
TOS (the original series) is good fun, but campy and inconsistent. For me it obviously has immense nostalgia value, but for a newcomer it's probably left for later. Deep Space 9 (DS9) is probably the most mature and narratively satisfying series and benefits from relatively modern effects work. TNG (Next Generation) is a little dated and doesn't really get to it's best until season 3. Enterprise seems to be a marmite show - people either love or hate it - personally I loved it. Voyager can be great at it's best but has plenty of filler and relies heavily on techno babble. Discovery, the latest show is brilliant IMO and could be watched as a standalone.
For a noob, I'd start with TNG but be patient with the first 40 or so episodes which are mixed in quality. Next DS9, then TOS, Voyager, Enterprise then finish off with a treat - Discovery.
If you like Sci Fi then it's definitely worth watching. It's one of the biggest cultural touchstones of television and of Sci fi. Be patient with it's slower moments and you'll be rewarded with some great story telling and iconic characters.
And when you watch "Spock's Brain" treat it as a comedy