The President should fly around on something small and agile (relatively speaking). Something like a Gulfstream G650. With the miniaturization of electronics, you don’t need a 747 to haul around communications gear.
If the Air Force needs a flying command post, that is a separate mission.
And the Press Corps can fly commercial.
The present AF one has counter measures like flares to head off IR missiles, and other stuff. Also need loads of communications gear to break through jamming, etc. So, maybe a C-130 sized aircraft would be the minimum size needed.
The G650ER certainly has the range.
The Presidents plane needs four engines to generate the power required for the comms, etc..