Zero Military, all the way. As the Korx or the Humans, I focus on economy, science, diplomacy, and building up infrastructure. With said priorities, the POTENTIAL to build high quality military rapidly is always there, but I'm not paying maintenance costs on fleets when I dont need them, and I am channelling most of my production into social/planetary projects. When I am not at war, constructors are about the only ships I build.
Diplomacy is key to this strategy (you have to spend customization points on diplo when playing the Korx). It is crazy, but even with only a few defenders, races of opposite alignment will (typically) just grin stupidly at you if your diplomacy is high enough. Then, you have technologies to give as cookies if things start detiorating. With diplomacy, you can nab other civs econ and research treaties and peddle yours away to those who would-be most hostile.
When and if war comes, you typically need a lot fewer ships because of your higher technology. Its not unusual to see one of my fleets go through 4-5 enemy fleets, simply because I focused on climbing the tech tree before building any ships.
A few side-notes:
-Starbases seem to weigh in as military power as far as the AI is concerned, so get those starbase fortification techs to give yourself a bit of muscle that the computer can recognize.
-When you don't have the fire-power, buy it with a few technologies. For example, need to take out a minor race's starbase because you want the resource? Park a constructor near the resource and get your closest neighbor to do it for you (especially if you have treaties from the minor race that you dont want to betray). Someone declare war on you and you are in an awkward state of developing infrastructure? Convince someone else to go to war and buy yourself a little time.
-NEUTRALITY is the alignment of diplomacy, NOT good, as many players seem to think. Buy it later in the game if you have to. Neutrality also gives you neutrality learning centers and more trade routes.
-Speaking of trade routes, use them to loosen up aggressive races aggro. They will start to like you when a percentage of their income comes from trade with you.
Where do you go from there? Well...this strategy is pretty versatile, allowing for alliance victory or technological victory fairly easily. An influence victory becomes very possible with all your research/tech and constructors running around. The conquest victory is probably most difficult, simply because you have to have patience, waiting until your technology and economic lead is large enough to start producing starships in earnest.
All of this said, I think that it is too easy to win this way. The computer SHOULD aggro harder on a zero military wierdo. Its not unusual for me to get through massochistic, obscene, or suicidal difficulty level games without fighting in a SINGLE war I didn't intentionally provoke myself. I hope future tweaks in the game will make this strategy more challenging (but not unplayable).