@Master Bruce So, one question that occurs to me. Being that the Lanterns are working for S.H.I.E.L.D. Who is actually in charge of S.H.I.E.L.D. at the moment? Or would it be better to just gloss over the actual higher ups at the moment? Just refer to the higher ups they get orders from as "The ever elusive boss who doesn't trust the Alien and the Jet Jockey and their magic rings he got dumped with by the President" or would Nick Fury or Maria Hill or another agent be alright to use? Speaking of, also, who is the current US President in the game? Please can it be Prez?
It'd probably be better to gloss over the higher ups, if possible. Makes things easier for any crossovers you'd want to plan out in the future, or if anyone else wanted to utilize SHIELD and had specific ideas. Then I'd say you and that player could figure out a specific director to go with. I don't have much of a preference.
As far as President, right now I'd stick with Biden and see what happens from there. It plays more into the idea that this is more or less our world (with mutants) until the week this starts in, when everything changes and history takes a different course. When a new President is elected, then we can go with someone from the comics.