Once you have built your science ships it's time to start thinking about building colony ships to expand your empire. If you didn't overbuild on the first turn, then on the second turn build at least one colony ship. You might also want to consider building an attack ship to protect the col; you'll hate yourself if your enemy's BR-1 scout explores into the system you're trying to colonize and destroys your colony ship. On the other hand, you might take that risk and save the cost of building an both an attack ship and a colony ship. Much of this decision depends on your own playing style.
This is another of those decisions that fall under personal playing style. Building the attack is the safe bet, but is not always necessary. There is usually, and almost always in a large-map game, safe planets somewhere behind your home world where you can send an unprotected colony ship. This then allows you to colonize the safe havens with your BR-1s and then move out toward the enemy with BR-2s a few rounds later. (Note, however that this gives the distinct disadvantage of not advancing towards your enemy, which can be costly further into the game.) If you play a type of game that tends to keep the tech development low, though, you might be better off by not spending the resources on the attacks for protection.
A modified version of the build-to-protect gambit would be to build two colony ships rather than one attack and one colony. The colony ships would therefore be able to protect one another for at least a short period before the first one is lost to colonization. You could either plant one colony on the first planet and allow the second to go on alone, or move both up to the furthest planet you wish to colonize, leave the second in place for protection while the first colonizes, and then retreat it back toward your home world to colonize one of the planets your advance had skipped.
What happens next depends greatly on the map setup and whether or not you have met one of the other players. In any case, you should get your remaining colonies, as well as those belonging to nearby enemies if possible, settled as soon as you can. Remember, the three keys to economic success in the early game are "colonization, colonization, and colonization." It may be in your best interest to skip over the small planets and colonize the large ones first, but be sure to go back and pick the rest of them up as the game goes on.
One exception to this is that if you can work out a planet-swapping arrangement with an ally. It is very often beneficial to colonize planets in each other's space so that you will both be able to build in or stargate to the other's territory and get ships there quickly.