james217 has it right, and as Zardoz mentions, designating one of your better planets as the research capital can pay off (assuming you have the economy to fund the research). Two things worth emphasizing from james217's reply are (1) it's ok, possibly ideal, to go many turns at the beginning without researching weapons technologies, and instead (2) use these resources to heavily invest in social production and planet/resource grabbing. The best way to research advanced techs fast is to spend the beginning of the game establishing strong planets.
I've found that, with strong planets and about 15 turns, I can go from having made no investment of my own in military techs to having competitive or superior ships. That is to say, in the beginning of the game, before any wars have popped off and no one has yet researched Planetary Invasion. So I grab resources, build up, and research planetary improvement technologies until about 15 turns before I think I'll be attacked or (easier to predict) 15 turns before I want to take out a neighbor. When it's time to gear up for war, I pull the social production slider down to a modest level and pump research and, as needed, military. Like james217 said, blitz the research tree. Medium hulls are a big boost over small; large and massive hulls do make a significant difference but may not be necessary--it's perfectly reasonable to fight the major battles in the game before reaching large hulls.