I have several starbases just like that in my empire right now. Step 1, max out the mineing. Step 2, if the starbase is in a sector near enemy space (because there seems to be some boost to a sector's influence based on adjacent sectors), then max out the Culture. Step 3, if trade ships pass through, bump up the trading posts (earlier if cash strapped). Step 4 depends on relative military strength. I always garrison resource starbases, and if my ships are superior, two ships by themselves are enough. If they're not superior then I'll add defense and military modules.
But yeah...ESPECIALLY a military star base. Losing any base can hurt you (morale and econ in particular) but losing a Military base is the worst...the last thing you want when in the middle of a war is to have the enemies ship suddenly get stronger relative to yours. Those are always my most strongly defended.
In my current game I now have 4 fully tricked out Military star bases and my Overlords have over 500 HPs and 60-something attack ratings.
Note #1: On big maps with lots of empty space, scouts are your friend. I found several resources 3 or 4 sectors away from the nearest star.
Note #2: When two nieghbors go to war, park a capital ship and a constructor next to each of their starbases you can get to. When one side blows the other sides starbase up, you're ready to move in with a constructor and garrison ship to take it. Picked up a Research and a Military starbase from the Altarians that way(who were winning) after bribing the Arceans to attack them.