John Ringo came up with a very compelling explanation why his VORPAL BLADE spaceship would be run by the Navy (Above and beyond the fact it was a converted nuclear missile sub). The point he made was that the Air Force is a sortie combat force whereas the Navy is designed around extended independent operations.
So the first question for a space-based military force is what theater it will operate in: near-earth, Moon, or deep space.
The second question is where they are based; earth, a space station, a moon base, or a mobile base.
If you're staying within the near future time-frame, mobile basing would be less likely.
One book that might spur some ideas is George Friedman's THE NEXT 100 YEARS.
The author is a geopolitical analyst at Stratfor, a policy consultancy.
One of the scenarios he presents for mid-century involves a series of military command and control space stations in geo-stationary orbit that require extended stays in orbit for the crew, which breaks with the Air Force's sortie operations mode, and thus justifies spinning off the Space Force as a separate branch.
If I were writing a story around such a base (he calls them BattleStars which "probably" would need changing...
) I would expect the crew to be involved in hypersonic drone piloting, communications monitoring, and orbital-systems cyber-warfare (hacking GPS constellations and/or spy satellites). The bases might be pretty good bases for orbital lasers to blind or destroy orbital assets. A bit further out, there might be a use for boarding parties to manned LEO space station or even sneak commando raids.
Such a branch would very quickly develop their own culture and jargon (if nothing else, to distinguish themselves from the earth-bound services) so there would be no need to get every last bit of existing military detail exactly right. (Less research needed.) Plus the required skillset might not have much to do with, say, Parris Island. Nerds in space!
BTW, one thing the Friedman book emphasizes is that tomorrow's antagonists need not be today's rivals. They can just as easily be today's friends and allies.