Connections... Vermiel had them, Shanahan (with the help of his dad) has them... Gruden has them...
McVay? The age thing isn't a knock except for the fact that he hasn't grown a long list of connections yet (not his fault, it's early in his career).
Pass on McVay for me... too risky.
I can see why that would concern you. But then again Mike Shanahan hired him and speaks highly of him, and Gruden has also been around a bit. It's like anything else, I think, where guys in a given environment know who's rising and when you're a dude like McVay you're gonna have interest from other coaches around the league who have coached against you or been in the division as well. The NFL is a pretty tight fraternity in that way.
And using your example of Vermiel... I love the dude but it's not like his connections led to a strong offensive staff right out the gate; he went with what he thought was a safe option that gave us a plodding and difficult to watch unit. So for myself what is more important is that in choosing a young rising offensive mind you are dedicated to growing him into the head coach you want, surrounding him with good talent and helping him make the required staff changes as you go forward.
IMO hiring Shanny, McDaniels, or McVay will give this team an offensive identity where they will have a consistent edge in gameplanning that cannot be hired away by other teams. No candidate is perfect, but I think all three are good coaches and deserving of the job, and if the Rams choose one of those guys and support them properly we're going to be in good hands.