I know that my opinion will don't be popular (and I'm really not sure of my own choice about the director), but I really would like to have David Lynch like director, why ? Simply because of Twin Peaks, I have read that he was a fan of Ditko spider-man, some characters, like Laura Palmer father, look like in some way Norman Osborn draw by Ditko, there are lot of others elements about my choice, but I don't want to spoiler for peoples who don't have seen twin peaks, I think that the others who have seen the TV show know of what I would like to talk.
I really like, in twin peaks, how he describe the teenagers, sometimes very bad and sometimes like they are pure and innocent and how they deal with the danger of the adult world, perfect for describe the self doubt of Peter Parker but also for the others characters, for example the Gwen Stacy from "Sins Past" remind me alot of Laura Palmer.
I think that David Lynch could do a great Spider-movie, of course, for that he should do accepted some commercial choice and to respect the comicbook (not too crazy things like he love to do), and to be honest, I don't know if he can control a blockbuster movie, but his quality it's that he know how to make together very fun moments with very intense and dark moments, for me it's his big quality.