Life support systems only have value for scouts, survey ships and freighters. For everything else you can build cheap constructors and lay out a route of starbases toward your goal. Once you conquer or settle a new planet in the region, you can decide whether to keep the starbases or scuttle them. And if it comes to war the AI will never attack a starbase - I've never seen it even try.
I used to always pick the miniaturization bonuses; now for weapons I usually pick a range extension and then some power increases. Miniaturization doesn't accomplish anything that a power increase doesn't - at least not that I can see. For engines, I always pick miniaturization. Adding +1 to movement is less valuable than being able to add a second (or third) engine. Get a logistics increase or two and you can put 50-100% more ships in a fleet than the AI can, and since combat is weighted in favor of numbers over quality, a large number of inferior ships will win (not that your ships are likely to be inferior). (By that I mean that 8 ships doing 5 points of damage apiece will fare better than 5 ships doing 8 largely because as a defense fails it absorbs all of the last shot - 5 in one case and 8 in the other - and because 8 small ships have more hull points than 5 small ships and so lose less firepower per hull destroyed). Not that you are likely to have inferior ships...
Seagoing warships once needed high tactical speed; nowadays they need to be able to steam at relatively high speeds for long distances (say, Norfolk, VA to the Persian Gulf). The relevant techs in GalCiv would be thrusters (which I never ever use unless I have 6 points I can't use any other way) and engines. If I can build ships that can get to the front in ten turns and the AI builds a ship of comparable power that moves half as fast, then assuming I can build as many ships I will probably win. The AI NEVER builds ships of comparable power to mine (it builds a lot of basic-level tiny-hull garbage) but my point is that high movement speed across the map allows you to get first to planets, resources, artifacts and to battle. And if you are fighting in the enemy's own space, superior speed allows you to take out multiple fleets, starbases and planetary defenses in one turn - and do it again the turn after, and then again until you invade and conquer.
The single 'constraint' on warship design in GC3 is having to put all three defenses on every combat hull (or deciding which one of the three you could live without). Getting a lead in research over the AI is tougher early on when you are covering the map with colony ships and constructors, but once you get settled and start researching techs to improve your research the AI can't keep up. Plus, it usually takes the 'wrong' choice, like reducing manufacturing cost. I have found that high weapons strength is less valuable than a range advantage, rapid-fire and stout defenses.
So far I haven't played on 'godlike' but at all of the lower levels I can out-settle, out-research and out-build the AI. I've had campaigns where my fleets of small and medium ships wipe out enemy armadas and never take a point of hull damage. That's gratifying - but not really fun. But to recap, I find that researching logistics techs, and having 2-3 engines and at least 1 of each defense on a warship, is the recipe for annihilating the AI.