The military graph is mostly only useful for AI diplomacy purposes. Just slap some guns on some ships and build plenty of them. Being effective militarily is a different story.
The most critical military engagements in the game usually take place early on, and your often going to be overmatched in Tech. Dealing with the opponents ships is easy enough to manage though, just build a star base and do everything you can to use the enhancements it provides.
If you plan on going on the offensive, I strongly reccomend getting the first two minuturization techs and impulse engines. Being able to move faster then the opposition is hugely important. From there I tend to throw an engine and some guns on a Small (NOT tiny) Hull. Lately, I have been favoring the Mass driver line of weapons since they tend to be cheaper then beam weapons, and the early missile weapons are too space intensive. It also helps to micro manage your fleets after fights, and pull the most injured back to a nearby planet to recover HP.
I tend to disregard defense until I hit Medium hulls. Once I get to medium Hulls, I will also start doubling up on my engines. Start using whichever defense is appropriate to your enemies prefered weapons tech, since it will often make a huge difference, even if you only have 1 or 2 points in it.
Against tough opponents, I can usually conquer my nearest neighbor early, and once I start grinding out medium hulls, I am in a dominant enough position that I dont really need to go to larger hulls to win the game.
The most critical thing to do with respect to having a strong military is to realize that its more important to be able to pound out new ships quickly then it is to have the latest and greatest tech. Rapid production will let you change gears quickly if your fleets get mowed down. By mid game, ships are expensive enough that your probably only building ships out of one or two primary production planets. Try to hold off building yoru manufacturing capitol until you either get at least a class 15 planet, or you find a class 5 or better with a precursor mine. Then surround that planet with 4 economy star bases and max out the bonus to production. You should be able to pound out your best possible ship within 2 or 3 turns at any and every point in the game.
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