B-52 wouldn't be a bad choice for airborne command since it has a pretty long loiter time (time it can fly around an area before going back for fuel).

On the other hand, it isn't really very well laid out for a large crew area. The Super Guppy being a mostly empty plane since it is for cargo makes this idea of it as a mobile base kinda neat. On the other hand, it has a pretty low loiter capability ( depending on loads it has a range of about 1/8 that of a B-52 or 747).

So yeah, I think it is mostly a style thing. If you want a "space plane" you are limited to a couple options.

1. National Aersopace Plane (NASP) designs like the X-30) https://en.wikipedia.org/wiki/Rockwell_X-30. Which would kinda wack the audience over the head with the idea since they were never really built or used.
2. Edge of space aircraft like the X-15, https://en.wikipedia.org/wiki/North_American_X-15 too small for a base.
3. The Pregnant Guppy / Super Guppy. Which they chose for looking stylish.
4. The Beluga, which is a jet aircraft that replaced the Guppy and doesn't look nearly as stylish. https://en.wikipedia.org/wiki/Airbus_Beluga
5. 747 used to carry the space shuttle. Which I think you avoid because without a shuttle on it, it just looks like a 747 with some bonus stabilizers and mounts on it. Plus, it invokes Air Force 1 more than space. https://en.wikipedia.org/wiki/Shuttle_Carrier_Aircraft. Plausibly you could do the 747-8 Dreamlifter, but that is really recent.
6. A military cargo plane with a spacey name, C-5 Galaxy or C-141 Starlifter. Again. Not as stylish by far since they would look like jumbo airliners to most people and relies entirely on the nickname. https://en.wikipedia.org/wiki/Lockheed_C-5_Galaxy, https://en.wikipedia.org/wiki/Lockheed_C-141_Starlifter
   

So style wise I think the Super Guppy is a no brainer with Beluga in close second for this show.