The relationship between Spock, Christopher Pike and Una-Chin Riley
A key aspect of the original series, especially with the two-part episode "The Menagerie" was the dynamics between Christopher Pike, Una-Chin Riley (Number One), and Spock. The trio were featured significantly on that episode and the pilot that they took the footage from. So clearly, any prequel series would have to look at and examine the story of why these three were so close.
Specifically the duo of Spock and Pike. After all, Spock nearly lost his spot in Starfleet because of his affection for Pike. Clearly, the two men had a bond that transcended that of a commanding officer and a subordinate. They were friends, if not closer to brothers. Something the show has done a good, but not great job of showing so far. We'd like to see more touching moments between Pike and Spock, but with more seasons to come, we're sure they're going to do just that.
As far as Una Chin-Riley goes, the original series hardly did the character any justice whatsoever. We've now found out so much more about this character thanks to Strange New Worlds. Thus giving us a greater understanding and respect for what is to come (and already came before).