Okay, a nice basic starting strategy is as follows:
* Immediately: Build cap-ship factory and set a capital ship going (I like the battleships, but colony ships will save you money). Build all resource extractors in the home grav-well
* Then: Build a few light frigates, and a colony ship if needed (i.e. if you went for one of the non-colony capships). Use these to claim surrounding worlds. 4 light-frigates alone will capture an asteroid without loss. The cap ship and (say) 6-8 light frigs should capture virtually any other worlds. Jump the cap-ship in a few seconds before the frigates, so the AI defenses will target it first (let it soak the damage).
* When you capture a planet, upgrade the civilian infrastructure by 2 points ASAP, or you will be bleeding cash. Try to build the resource asteroids quickly too.
* As you are expanding, build 2 civilian research labs and start researching economy-related stuff, or volcanic / ice planet capture abilities.
* Place a few static defense turrets in captured worlds which can border a neutral or AI-held world. This should stop the AI attacking quickly with a small and irritating force.
* I don't agree with the "upgrade your home planet immediately" ethos. Sure, you get an extra couple of credits per second, but it is expensive (750 /225 / 225) and that cash is extremely valuable at the start of the game. I would much prefer to put it into getting trade facilities earlier, and/or upgrades for newly captured planets. Upgrade the planet later, when things aren't quite so critical.
Enjoy!