My races tend to be the same, building up a powerful economic structure but neglecting serious military build up until either a war breaks out or until we get ahead enough in the technology curve to regularly field ships much larger and better equipped than the nearest equiv-tech neighbours... and then depending on the situation and who's been annoying me with threats and extortion the 'sleeping giant' might just decide to stop napping because of people poking it rather than a swift Pearl Harbour-esque awakening.
Do not poke sleeping giants... we're not morning people.
That said, occasionally I like to mix it up and concentrate on military first and ravage the galaxy before anyone else can put up a defence. It depends on my race and the situation and stuff.