OK. An "essential viewing, beginners guide, series in a season". If the OP doesn't mind I've included 26 as that is the average length of a TNG season. It's hurt me to keep some favourites out, but I'll try to explain my reasoning.
I tried to include all the major arcs - The Klingon civil war, Wesley's destiny, Tasha-Sela, the Cardassian and Bajoran arc with it's backstory to DS9, The Borg before they were "humanised" to their detriment in I Borg and Descent. Then I tried to include a character episode for each of the crew and threw in a couple of personal and fan favourites for good measure. I've left out Unification and Relics because, although I enjoy them, they are sentimental links to TOS and I wanted this list to stand on it's own as TNG.
Encounter at Farpoint
Certainly not the strongest beginning by a Trek crew, but introduces us to everyone and the formidable Q. Also included here because I think it's needed in order to assist the series finalé.
Where No One Has Gone Before
Included here because it seems to fit the most character development into the shortest time. Introduces the Traveller and shows how Wes becomes a bridge regular. Included for the first time watcher as it would make no sense to go directly from Yar's introduction in Encounter to her death in...
Skin of Evil
Included to explain Yar's death. An important part of upcoming episodes.
Elementary, Dear Data
I like this one. I know it's not in every fans top 25, and it is full of inconsistancies, but it's quite sentimental for me. It's the first episode I saw as a kid back in the eighties and got me hooked. Introduces the Moriarty character whom I like.
The Measure of a Man
Excellent drama. Riker pitted against his friend because of his duty. Data is recognised as sentient.
Q, Who?
Return of Q. Introduction of the Borg...
Who Watches the Watchers?
Explains the Prime Directive and why it is so important for a Starfleet officer to uphold.
Yesterday's Enterprise
I've always loved "What if's..". Return of Yar, backstory for Sela. Explanation of why Federation had to make peace with the Klingons. The Enterprise "C". The "D" as a warship. So good in so many ways.
Sins of the Father
Worf backstory. Beginning of Klingon arc.
Best of Both Worlds
Nothing to be said. TNG's finest (two) hour(s).
Family
Excellent conclusion to previous episode and it includes some great character development. Nicely shot too.
Reunion
Klingon civil war hots up. Worf goes boldly where no Starfleet officer has gone before by slaying a candidate for succession. We can almost forgive the introduction of Alexander.
The Wounded
Introduction to the Carddies and an episode in which O'Brien got to shine. Good story.
The Drumhead
Excellent commentary on Mcarthy era witch-hunts. And Worf gets sucked up in it. Trek at it's best.
Redemption
Memorable conclusion to the civil war, with the appearance of Tasha's daughter (she was heard, not seen in Mind's Eye). Nice sidestory about Data trying to be accepted as a Captain by his bigoted officer. Shame Worf found it so easy to resign his commission and get it back again. Would have been a nice way to say goodbye to a character (who in my opinion was rarely as good again).
Ensign Ro
Continuation of Cardassian arc and introduction of the Bajorans. Paved the way for the excellent DS9.
The First Duty
So Wes is human afterall. Never liked him until now. Good story about Starfleet principles.
The Inner Light
What might have been for Picard. The Ressikan Flute solo still brings a tear to my eye.
Chain of Command
"There are four lights!" Interesting look at a different Captain on the "D". And we finally get to see Deanna in a uniform, sexy and empowering.
Ship In A Bottle
As said earlier, this is a personal preference of mine and a conclusion to the earlier episode. I can forgive the oversights. Love Moriarty. Love Stephanie Beecham. Love Barclay saying "End program" at the end (how many of us did that too!)
Tapestry
Another "What if?..". Q comes up with the right mix of humour and pathos. Excellent.
Lessons
Oh, poor Jean-Luc, the life of a Starfleet Captain is a lonely one. Lovely conclusion, in some ways, of The Inner Light and an excellent exploration of what it means to devote your life to the Captains chair.
Second Chances
It was between this and Dark page for a Deanna story to show a first time watcher. I plumped for this because I didn't want to include any other Lwaxanna episode in order to explain her character, even though I think both actresses were great in Dark Page. This story has the added benefit of giving some kind of conclusion to the Riker - Troi romance that was begun in Farpoint.
Lower Decks
Such an interesting episode at the time. Told from a unique perspective. Part of the conclusion of The First Duty. I'm so glad they did what they did with the end. Life isn't all happy Hollywood endings...
Journeys End
We say goodbye to Wes and the traveller. Helps set up Voyagers premise.
All Good Things
"Burning the midnight petroleum". Best series finalé to date.
