Likewise, I've wanted this myself for quite some time, and have given it a great deal of thought.
Player Bases would be little different than the various Outposts or Buildings we track down during Surface Scan missions - small and simple things, largely inert, with the singular exception of a Universal Landing Pad (a single, large pad we can land any size ship on, without having to request docking).
Shipyard services would allow us to change ships, but would offer no ships for sale.
Outfitting would allow us to change or store modules, but would offer no modules for sale.
Repairs would be 15% more expensive.
Refueling would be 15% more expensive.
Reloading would be 15% more expensive.
Why? Because these are not stations supported by factions.
No commodities market.
No black market.
No power contacts.
No Interstellar Factions contacts.
A Facility Manager Contact would be able to provide services such as purchasing upgrades/additional functions.
The Mission Board would also have the Facility Manager as the sole mission giver.
Missions would be "Donation" missions - to haul in various commodities such as Hydrogen Fuel (to maintain fuel reserves), various Food and Beverage commodities, and various spare parts.
These would not garner any sort of reputation, influence or other standard rewards, but rather would maintain stock of supplies.
Defense turrets and skimmers could be added as Upgrades - to keep people from blocking your landing pad (though another player landing on someone else's pad would not be considered as "landed" and they would not have access to any of the services offered.
I see base supply levels being tracked in a manner similar to the way Power Play tracks things like Consolidation.
Actual Construction should go something like this:
A Site Module is purchased - a 1 Cargo Unit item, which is then taken to the location of a player's choice, loaded into an SRV, moved into position, dropped, nudged around, and finally Scanned to activate it.
This establishes the location of the base's Center, and the Site Module is then replaced with a basic Communication Tower that serves as something to lock on to when approaching the planet where this is located.
A landing pad is then spawned and can then be landed upon to access the Services menu.
At this point, only the Mission Board would be available, with a number of Resupply missions (donation type missions as mentioned above).
Hydrogen Fuel, Food, Water, various parts and the like would be offered until supply levels are brought up to "Minimum" levels and these services then become available.
Upgrades also become available from the Facility Manager contact.
Upgrades would include things like:
1. Power Generator - The first available upgrade, and requisite for all other upgrades.
2. Living Quarters - Adds a small building to the base to serve as a place to stay.
3. Biodome - Build a biodome to eliminates the Food Restock "missions".
4. Lights - add some decorative lights around the base.
5. Base Defenses - add turrets to keep unwanted visitors off your pad and out of your space. Works on wanted visitors too!
And so on...
So let's assume we've already completed the Generator construction, now we want to build a Living Quarters. After selecting this, the transaction panel shows a new Mission:
"Construct Living Quarters"
Bring supplies and materials to construct a Living Quarters at your base.
Iron: 100 Tons
Consumer Electronics: 10 tons
Domestic Appliances: 10 tons
Polymers: 200 tons
Copper: 50 tons
Structural Regulators: 5 tons
This would be completed similar to a Community Goal, though amounts of each commodity would be tracked, and once this order were completed, the new facility would be spawned at the base location.
Clearly a tremendous amount of development would have to go into this, making this a very distant addition, and it would be a huge time, effort and credit sink, but I also think it would prove to be quite rewarding as well. And by limiting the total functionality to refueling, repairing and outfitting (perhaps trophy gathering and displaying when we're able to walk around inside of things), it would "fit" in what Elite is - a game about pilots and their ships. Since these can't become "credit farms" or commerce hubs, they don't take away from what stations and outposts are.
And I think the "recipe" method for construction also ensures that any far distant constructions, while still possible, would become something of a personal monument of achievement - just imagine hauling all these materials out 30k light years to complete construction on some lone outpost, on some distant plateau of some world on the fringe of the galaxy itself!