I think that's great, Beholden! If you want to get to know him, maybe tell him a bit about yourself? I have found doing my genealogy work that there's lots of "interests" and capabilities that are inherited and interesting occupations that seem to go down the family tree. Have you seen a picture? Maybe comment on your parents, siblings, grandparents he might look a bit like?
I have three grown stepsons, two of whom were starting their 20's when I "met" them. Rather than concentrate on the nerve-racking fact that he's your grandson and you don't know him yet, just try to talk to him like you would a young man of that age; about his interests, does he have a girlfriend, etc. Put as much of your personality in the interaction as you can for whatever modality it is; when I call one grandson at his office, the secretary answers and invariably asks who's calling and I answer, "His wicked stepmother"