Personally, I want everything but not necessarily at the same time.
1. Able to be constructed anywhere, even uncolonizable planets/asteroid belts.
-a sort of remote/combat construction frigate could be built, sent to a location where it would start construction... construction would be supplied by trade/refinery/supply ships that would bring the resources to your location to be used by the constructor, therefore construction would be more costly and take longer if ememy somehow destroys supply ships and steals the resourses from them.
2. basic needs. guns and strikecraft
3. highly customizable, similar to capships, but would also require resources to level up. exo may or may not reduce upgrade credit cost.
4.Being customizable, you would have many options.
Ion cannons and other capship like abilities
Internal repair bays that would protect or store weak or damaged ships and repair them if needed
Also all other ship abilities should be considered as options, such as repulsion, shield sharing, etc.
Logistic structure of your choice built in, or at least a partially functional version of chosen logistic structure.
abilities of other defensive structures as options.
Culture Repulsion standard,... this comes standard with big ships, and this is a big defensive item, so it makes sense

I'm just afraid if we don't have ideas, we could get boring/generic star bases dumped on us.