Star Trek: The Next Generation (TNG) is one of the most popular shows in the franchise (and definitely meme'd to death online). With a stellar cast, interesting development of characters, and fascinating action and psychological stories, it helped build a modern setting for the franchise to grow into.

Also, it's one of the only series that received a modern sequel series (Star Trek: Picard). Sure, there are occasional crossover episodes between series, but TNG was so popular, they got most of the old cast back to reprise their roles decades later. So if you're invested in the characters of TNG, you get to see what adventures they're up to years after leaving Starfleet.

ALSO also... TOS and TNG are the only two series to get full-length feature films made alongside their respective TV shows. (Even the modern reboot films are set in the TOS timeline, following the characters from that show.) So if you'd like to see TV show characters on the big screen, TNG will give you those big budget productions along with your show.

The first TNG film (Star Trek: Generations) actually has Captain Picard running into Captain Kirk from TOS, who got stuck in some sort of time anomaly in space. It was awesome that they found a way to do a crossover between the two series, considering they take place almost 100 years apart from each other in the Star Trek timeline.