I dislike the idea that ships are purely military. Yes the way GC does the economy all shipyard production is controlled by the military production slider... but this is already a misnomer as colony ships are not military.. nor are freighters, or survey ships etc...
In thinking about it more I think the best option would be to be able to build permanent "factory ships" that can go out and build stations.
The factory ship constructors can be given several options.
A build starbase (200credits)
B Build starport (150 credits)
C Upgrade starbase (credits based on the type of upgrade)
D. Build supply ship (100 Credits)
Supply ships would function based on the current tech level and scale with improvements but in general you would then link x starbase or starport with y planet. the support ship level could be set based on the logistics level of the empire and would function similar to the current trade links.
Building more supply ships creates more supply to the starbase. the "upgrades" would then be build in a build queue similar to the starports and could be rushed just like any other build feature.
Once a starbase is fully upgraded the excess support ships can be assigned to a new starbase... or can be sold for scrap, or used to support military/civil/social projects and boost the power of the station.
This would also allow starports to be supported by multiple planets that are currently "outside the cost effective range" of the planets supporting it. It would only requre the player to build the support network.
Yes this increases the micromanagement to a level... but it also lowers the ship spam and makes for strategic choices for support and supply.