Here’s five of my favorites, especially because most of them provide some character lore/development that enhances watching the movies:
The Corbomite Maneuver - Kirk’s captaincy style
Amok Time - Spock lore
Journey to Babel - fun, ethical dilemma episode, introduces Sarek
Let That Be Your Last Battlefield - moral lesson episode, introduces the self-destruct, and I’ve found that modern viewers are fascinated by the fact that racism has become alien and confusing to future humans
The Galileo Seven - character drama, features Spock making survival choices that weigh the needs of the many against the needs of the few