Welcome to the Forums and the world of Vintage Airstream/Argosy ownership!
I have towed my '64 Overlander all over the country with my '99 GMC K2500 Suburban, and am confident that you will like your combination of 26' Argosy/C-K 2500 Suburban (my Suburban currently has nearly 119,000 miles over half of which have been towing either the Overlander or Minuet). I suspect that the loaded weight of you Argosy will likely approach 6,000 pounds as my '26 Airstream Overlander when loaded is within close proximity to that weight with a tongue weight of about 725 to 750 pounds depending upon how the coach is loaded.
I have utilized the Reese Straight-Line hitch (it includes the Dual Cam Sway Control System) with 800 pound weight distribution bars since 1995. While there are many similar systems produced by other manufacturers, I have been very well satified with this arrangment. The one thing to keep in mind if you choose to go with the Reese Dual Cam system is that it is sensitive to having weight distribution bars that are very close in rating to the actual tongue weight of the trailer - - I have found this especially true when towing with my K2500 Suburban.
I currently use a Tekonsha Voyager Brake Controller on the Suburban, but would probably switch to the Prodigy if I were reconfiguring the system today. On my Cadillac, I utilize the same hitch system, but utilize a Hayes-Lemmerz MicroControl HD Plus controller with remote control - - I am very satisfied with this inertia type controller, but it is not a widely respected controller as is the Prodigy.
You can find more information about brake controllers from:
Hayes-Lemmerz MicroControl HD Plus
Tekonsha Brake Controllers
Good luck with your Argosy/Suburban combination!