To watch all of The Star Trek franchise, it would take you nearly a month of no-sleep-marathoning. Nearly 550 hours at this point. Twenty-four days. AND THEY'RE STILL MAKING MORE. You don't have that kind of time.
I've attempted to put together a much more condensed series of Star Trek. Dividing it into ten episode seasons. For the most part, these are My Favorite Episodes. I've left out some that are historically important episodes, in favor of things that I found fun to watch. If you're a Trekkie or Trekker, or just consider yourself a fan, I may have left off your favorite episode. Sorry. But this is more a list for people like me, who had seen an episode here and there, were interested in seeing more, but don't want to invest in the whole 530+ hours. I'm doing it, so others don't have to.
Season Four saw TNG mainly through the lens of Data, and Season Five was Worf-heavy. In watching the beginning of TNG, I thought I'd misremembered Picard. He was as much a lucky, mostly incompetent buffoon as Kirk was in TOS. But, unlike his counterpart, Picard makes fewer and lesser mistakes as the series evolves. We also get to see the family dynamic of the crew in a way that we didn't quite get with TOS, which focused almost exclusively on Kirk/Spock, Kirk/McCoy, Spock/McCoy.
Much of this season also focuses on new alien races, some which will become prominent later in the continuity, and some which we will never encounter again. And, unlike the previous two seasons in this chronology, there is no intended story arc to this season. This is just interesting sci-fi from a crew you, hopefully, already like.
Episode 1: First Contact
(Picard, Riker, Troi, Crusher, Data, Worf)
Prime Directive episodes are usually tedious interactions where different crew members argue over whether or not to help some world that they probably imperiled in the first place. I've spared you from most of them. In this episode, they've pretty much been caught violating The Prime Directive, despite their best efforts to blend in to an alien populace. This is a damage control episode where the crew tries to work diplomatically to rescue Riker, who was undercover as a Malcorian. There's a lot of American political allegory that is still, sadly, relevant, twenty-six years after this episode aired, but it's not as heavy handed as Star Trek allegory often is.
Episode 2: Allegiance
(Picard, Riker, Crusher, Troi, Worf, Laforge, Data, Wesley)
It wasn't so long ago that Picard was captured by The Borg and assimilated, so you'd think they'd up security on The Enterprise, but, no, I am unsure if there is a single season where whomever is captaining The Enterprise at any given moment, isn't abducted by someone he can't identify (or Q, it is often Q). This episode serves as a morality play for Picard while the rest of the crew contends with a mostly ineffectual Picard doppelganger.
Episode 3: Future Imperfect
(Riker, Picard, Crusher, Laforge, Data, Worf, Troi)
After a noxious gas incident with Worf and Laforge, Riker wakes up to discover he's forgotten sixteen years of his life, and he's now Captain of The Enterprise. This is what Kirk would have called a Tuesday. Will this episode mean the entire chronology jumps forward sixteen years?
Episode 4: Tin Man
(Troi, Picard, Data, Riker, Laforge, Wesley)
Despite being an ensemble-focused show, most TNG episodes have one character at the core of its storyline. Picard, Riker, and Worf stories are usually fantastic (after season two), Data and Crusher stories are interesting, Wesley stories can grate, Troi stories are insufferable, and Laforge stories are always focused on how much he sucks, even though he's fun and competent as a secondary character. This is, so far, the only Troi episode I've made it all the way through, and I quite enjoyed it. Another Betazoid joins the crew to learn about a seemingly sentient spaceship. There's an interesting angle with Data, some Romulans cause havoc, all-in-all, it's just a solid episode where the writers finally make interesting use of Troi.
Episode 5: Darmok
(Picard, Riker, Troi, Worf, Data, Laforge, Crusher)
I feel this episode is best if, like the characters, you have no idea what you're getting into. It's my favorite episode of the season.
Episode 6: Ensign Ro
(Picard, Ro, Guinan, Riker, Data, Worf, Crusher, Troi, Laforge)
Starfleet shenanigans put a court martialed officer of a race made refugee by The Cardassians (who we are seeing for the first time in this chronology, but who will be hugely important as we progress). It's an interesting look at prejudice, and how politicians use terrorism and tragedy for their own ends. Something Star Trek often attempts, but rarely pulls off.
Episode 7: Disaster
(Picard, O'Brien, Ro, Troi, Riker, Data, Crusher, Laforge, Worf)
Several disaster movie cliches are overlapped in the most character-driven episode since Family. The O'Brien/Ro/Troi interplay is my favorite non-main character study so far in the chronology. Also, it's nice to see a story where kids are just annoying children as opposed to spooky, powerful menaces.
Episode 8: The Game
(Wesley, Riker, Picard, Crusher, Data, Laforge, Worf, O'Brien)
The idea that games in the twenty-fourth century would look like a version of golf they designed for WIndows 3.0 is quaint. This is an actually fun Wesley-focused episode. Wesley actually left the series previous to this episode but his send-off episode is Terrible. So, this will be our sayonara to Wesley Crusher. It's the episode that the annoying boy genius deserves. It's also a heavy handed treatise on the addictiveness of video games, but it's So Ridiculous and Over The Top that it's hard to be annoyed by it.
Episode 9: A Matter Of Time
(Picard, Crusher, Riker, Data, Laforge, Worf, Troi)
An annoying time traveler (Max Headroom...aka Dr. Leekie from Orphan Black) shows up to observe what he claims is a pivotal mission for The Enterprise. It's a fun twist on a Prime Directive episode as the crew are the ones being kept in the dark to preserve the time continuum Or Whatever. It's mainly fun to watch an actor portray an annoying character and not have it be agonizing to watch.
Episode 10: Redemption
(Worf, Picard, Guinan, Data, Riker, Yar)
After all these one-off adventures, we finally tie into a major storyline, as we revisit the chaos of The Klingon empire. It's a direct sequel to Reunion, though much time has elapsed. It's a satisfying conclusion(?) to the story arc begun in Sins Of The Father, and a fine way to leave this season.
I'm not including five bonus episodes for this season, as there is no story arc to flesh out, and there is a massive drop in quality between the good episodes and the average episodes of this era of TNG.