A bunch of thoughts came crowding through my head while reading the OP, lemme see if I can organize them all here.
When you're doing the initial land grab, what are you rushing with money? Colony ships? What else....? You see, when I colonize a new planet, the first thing I do with it is rush two factories. Otherwise the planet will be totally useless for six months, until that first factory gets built. What you need is not planets--but PRODUCTIVE planets. Rush a factory or two in order to get your infrastructure built out faster. And keep them once they're built. You'll need them throughout the game to upgrade your buildings.
Once any given planet has two or three factories, strongly consider piling laboratories onto all the other tiles. Yes, on ALL your planets. The lab you get at game start is cheap to build; pile in lots of them and do some tech rushing. Then start replacing them with other stuff when needed.
Think specialized planets. Instead of building a few labs and factories on each world, pick one planet and build nothing but factories on it. Then put your Manufacturing Capital there. On another planet, build nothing but research labs--and the Tech Capital. If I run across a planet with a food bonus tile or happiness bonus tile (or preferably both), I put up a farm, a couple of happiness buildings, and lots of marketplaces--i.e. a specialized money planet.
Consider rushing the Sensors tree and putting up a quick batch of picket ships. I've gotten away with rushing to the top (Sensors Mk 4) at the very start of a game, but you can get effective perimeter sentries without going that far. Position your sentries so you can spot an incoming threat well in advance (if you get Sensors Mk 4, and pile lots of them onto a Cargo-type hull, you'll have a ship that can see the entire map). If you see nothing on the radar, relax and develop your economy. If and when the bad guys come along, you're going to know exactly where and when, and how much force you need to counter them. Advance intel is worth a LOT--a small fleet in the right place will do you a lot more than a huge fleet in the wrong place.
Also consider an early run for Interstellar Republic. It's not a long trip to get there, and changing to a Republic will give you a 25% bonus on ALL your spending. Military, social, and (most important!) research.
In the early game, think technology and economy rather than military. Get your economy running first, and research the technologies needed to do that. Think factories, morale, and soil enhancement (hold that last one until you've used up most of the available space on your planets). AVOID researching "Research Academies" until your planets are well-developed and you're prepared for a long stretch of social spending--a Research Academy costs about three times as much as a research center, and only gives 2 more research points. You'll have to do it eventually, but if you do it too early, you'll sink your economy faster than a singularity driver will an inflatable raft.
