I saw all the TOS Movies and five seasons' worth of TNG before I first saw TOS itself in the early-'90s. These were my first reactions to the main Klingon episodes at the time...
"Errand of Mercy" --> Disappointing. "There aren't Klingons!"
"The Trouble WIth Tribbles" --> Fun! No real opinion about how Klingon they are.
"Day of the Dove" --> Love this episode! These are Klingons!
The Klingons in "Day of the Dove" fit better what I think of as Klingons. It took a while for TOS to get there.
Then The Search for Spock came and ran with it. That movie solidified what I think of as 23rd Century Klingons. Obviously TMP gave them the look, but it was TSFS that perfected it. TSFS is where it all came together. Then TVH added the finishing touches with the Klingon Ambassador.
My opinion of "Errand of Mercy" has gone up with time. But that's only because I got over the initial shock I had when I first watched the episode. Going in, it wasn't what I thought it was going to be.
How Kor, Koloth, and Kang translated into DS9 backs up my point. Kang didn't change at all (not including makeup design or being older), Kor changed a little, and Koloth basically had to be remade from scratch.
DSC Klingons -- outside of the makeup -- feel in line with "Day of the Dove" and the TOS Movies. They're distrusting of Humans, think Humans are out to destroy their way of life, have a way of spinning facts to their advantage, and only respect strength. They also use the Klingon Disguised As Human idea from "The Trouble With Tribbles". The idea that battle is glorious, that Kor first said in "Errand of Mercy", I don't get a sense DSC Klingons think battle is glorious until "Such Sweet Sorrow".