The approach that I found most helpful for an early start that gives you a very good eco and a very decent fleet to defend with and continue expanding with is the following:
- Build mining stations, produce 2 or 3 Seeker Vessels (depending on map size) on auto-explore, and 1 Missionary Vessel;
- Build a Capital Ship factory and produce a Halcyon Carrier. Upgrade the Adept Drone Anima. Produce 4 fighter squadrons;
- Drain your population count by building as many Disciple Vessels as possible;
- Begin colonizing in all directions 2 jumps away from your home planet. Colonize using your entire fleet and do only one jump at a time with the entire fleet. Don't divide your fleet;
- Once colonized, upgrade infrastructure to max;
- In the meantime when the above colonization process is under way, whenever your resources permit, build 2 Temples of Harmony, upgrade fleet capacity and number of capital ships. Research planet types as necessary and research eco improvement rates for mining;
- As soon as you can afford it, build a second Halcyon Carrier, this time upgrading it with only bomber squadrons, and attach it to your main fleet;
- Upgrade Capital Ships again and build a Radiance Battleship and attach it to your main fleet;
- Build frigate factories and defenses on the periphery colonies and trade ports on the inner colonies.
- Continue expanding slowly, but also heavily fortifying your periphery.
For the Halcyon Carriers, when you have the chance, just upgrade the Adept Drone Anima. This is more important for early game. At this point you'll want to start building cruisers instead of upgrading to better frigates.
If no enemies are forthcoming, then it's at this point that I slow the pace significantly down and focus heavily on research and fortifying while slowly continuing to expand. My first upgrades tend to be towards improving mining and tradeports.
You don't want to stress just eco because then you'll get wiped out if anyone invades. In early game, it is much more powerful to defend your colonies with a well-armed fleet than with purely static defenses, even if you have to jump your fleet around. Initially, static defenses are just a drain on your economy. If you're playing against harder AI, if they invade early game, it will usually be with at least 2 Capital Ships and a sizeable fleet, hence the second Halcyon Carrier with bombers (supplemented with Aeria Drone Hosts).
Think of it this way: if you set an aggressive AI, then they will concentrate more on building fleets than defences. There is no way that you can outmatch an aggressive AI fleet with purely defensive upgrades this early on in the game. You just don't have the eco to support this. So your best bet is to outmatch them offensively. Even though the AI may have a better fleet than you, it will suffer a lot of damage. You'll definitely be able to take out their capital ships, in which case the remaining fleet will most likely retreat. On the other hand, if you have a defensive AI, then they wont be attacking you early on. Therefore, you don't have to worry about building defences early on. The better the offensive fleet, the quicker you can colonize and getting a good eco start.