I play DA and a little different strategy, usually going for a tech or alliance victory. As a result, I focus my fleet on being strong enough to deter attack, but not necessarily strong enough for a military victory.
In the early game, most of my effort is focused on economy and research. Once I see someone registering on the military power graph, I focus research to get missiles and first level mini. I then build a tiny hull with one missile and pump several of those into orbit around most planets, until my military rating is #1 or #2. Then I put some effort into building up to the next level of missiles. Once I get to the missile that does 2 damage, and I see that my mil rating has dropped a bit, I do a fleet upgrade and double my military power overnight. If you also put some research time into mini. and armor, you can do this mass upgrade a couple of times and stay on top militarily through the early to mid game, without using many production resources on warships.
I usually spend my early military production on colony ships and constructors. As an extender for the tiny ship strategy, if you equip your starbases with ship support, you can substantially boost the power of a swarm of tiny ships. Of course, the best effect is in local defense, but if your military rating stays high, the AIs will fight each other until it's too late to stop you.
Once my research is really going, I'll push development of missiles and armor. An anti-matter torp on a tiny hull, plus some starbase support and a swarm of these drones will keep the AIs friendly for a while. At least long enough to build a good fleet of large hulls....