My best Battlestation ever was a Mining Station (I think it was on Economic Enhancement). I like to play massive maps with few stars and planets and slow technology, so space is more terrain like (and I think more strategic)
I built one and the Drengin started threatening, since it was the closest to them, I upgraded the station with some defenses. sure enough, the Drengin attack a bit later and they go for my mining station. It survives, wiping out a minor fleet, but is heavily damaged. Well I don't want it to die after such a valiant effort, so I upgrade it with all my nearest S9 (speed 9) constructors, and it survives the next attack by the Drengin. They become fixated on the ship (which I've by now renamed Drengin Frontier DS (for defensive station). I max out that ship and give it a bit of low end support with what I call Frigates (small frames, slow, with the best weaponry available at that time). That station held up for the entire game, and is the reason I eventually was able to beat the Drengin. Allowing me to reach their territory and destroying possibly hundreds of their fanaticly obsessed ships. It was a really fun game.
In the game, I'd like it if ships healed faster when in a Military Stations radius, and if it were cheaper to upgrade them then (or perhaps ONLY possible to upgrade them then or when on a planet with a yard.