The linked obit strangely doesn't really make it clear that Barrett did the voice of the Enterprise computer in the original series as well as TNG and other spinoffs.
I loved her in that first pilot, where she played the first officer to Jeffrey Hunter's Captain Pike. Her character, though human, was intellectual and unemotional, qualities that Spock's character would take on when he became the first officer in the second pilot. In the first pilot, Spock was still played by Nimoy, still a Vulcan, but was third-in-command at most, and just as emotional as any human (he even smiles!)