Since it was a Star Wars fan (original trilogy) that needed to be "turned" I agree that the cat-and-mouse play of "Balance of Terror" was (obviously) a good choice as it's similar to events in "The Empire Strikes Back".
"The Corbomite Maneuver" (it was the first regular episode of TOS, most impressive!) revealed that Captain Kirk wouldn't have been up to play a game of poker with Han Solo. Understandably the ghost of Bill Shatner told the protagonist in Meyer-Burnett's "Free Enterprise" to kick the butt of the Star Wars antagonist who claimed Han Solo was cooler than Captain Kirk (
Can you believe that?).
And then there is "The Doomsday-Machine" that obviously came before the Death Star of Star Wars. Another concept pretty palatable to a Star Wars fan and revealing that some ideas of Star Wars had been there first in TOS (even if the VFX, admittedly, didn't look that great).