According to Deak Slayton, head of the Astronaut corps, Grissom would have been his choice to be the first to walk on the Moon.
There was a general feeling throughout NASA that one of the original seven should be the first to walk on the moon. Besides being superbly qualified, Gus was in the cat bird’s seat by default.
Shepard, Glenn, and Slayton all had medical issues they were dealing with. Carpenter got cross wise with NASA brass and never flew again after Mercury. Schirra and Cooper had falling outs with various people in NASA. Shirra did make the first Apollo flight but never flew again. Cooper was supposed to fly on an Apollo mission but was bumped over some kind of disagreement.
There is little doubt that Gus would have been the hands down favorite of both management and the astronaut core to land first had he lived. And while he is not mentioned as much, White was also high on everyone’s list and probably would have gone with Gus on his second Apollo flight as well had they both survived the first one.