Best thing you can do for your economy is expand as fast as possible...on large maps, always lead with a colony capital ship (akkan, progenitor, jarrasul) and try to expand in two directions: one direction with the colony cap (and a few scouts) and another direction with a normal colony ship, a few light frigates (cobalts, disciples, skirmishers) and several scouts...

The scout ships actually are highly effective at killing the krosov siege frigates around the planet (though you will need to turn autoattack on), and once those are dead you can colonize right away....first thing you should build then at the planet is a turret or 2 (maybe 3 if a planet with 2 Kodiaks) which can kill the rest of the militia and allow your small expansion fleet to move on...occasionally the planet will have a small militia (asteroid, moon, barren, and some ice/volcanics), and so instead of wasting money on a turret you can just use your light frigates to kill the militia...

Next best way to buff your economy is to build trade ports....they pay for themselves quite fast and don't require that many labs for TEC and Advent...spam them on planets best suited for industrial specialization like volcanics or on planets with lots of logistic slots like deserts and barrens...put your labs and culture on planets best suited for high population like terran, ocean, and ice...

If you know the map is roomy, build social specialization on your HW ASAP and scuttle your 2nd frigate factory (and capital ship factory after first one is built)...you can always research economic techs like meta/crystal and population, but those don't pay off as fast as trade ports and so are of secondary importance...

Basic strategy isn't much different between races when it comes to expansion...Vasari have advantage that their scouts can take neutral extractors, and the other races have better frigates...only real difference is that for Advent and Vasari you will get culture on HW first before trade, and TEC you'll go trade first...

There is no need to build any refineries....only reason you even research the tech is because it is a prerequisite to other techs...

For strikecraft, all bombers is best if you are trying to kill an SB, cap, or titan, and the enemy has no counters (corvettes and fighter spam)...otherwise, you are usually better spamming fighters....

If you are Advent or TEC, always get at least one military lab early on for Corvettes; they are fast and good against siege frigates so they are good for clearing out neutral planets and are a powerful combo with Light Frigates early game. After I usually go for 2 civic labs for planet exploration techs, but as TEC this will also get you trade ports. Advent will need one more lab for trade.

I wouldn't rush specifically to get them, but if you end up getting enough civic labs for them while trying to get other things and have some spare resources to invest, go and put one culture center down in a central location in your Empire. Culture doesn't contribute to your economy as much as trade but it has other bonuses.

In pure economic utility, Trade Ports > Culture > Refineries.

Sure, a planet with three tradeports makes 3 times as much credits as a planet with one trade port. Late game you will have many planets with lots of trade ports. However, even better than building a trade port at an existing planet is to build a trade port at a new planet that expands your trade chain. This will increase the trade income of all trade ports in your empire, as well as giving you the money from the new trade port.

Sadly if you just play the base game refineries are rarely any good. You need a centrally located planet with many phase lane connection to planets with lots of resource extractors (preferably non-colonizeable gravity wells) to make refineries work. On large maps especially, where you can get very long trade chains, trade ports are almost always better. You would not be a bad Sins player if you just always go for trade instead of refineries, since there are relatively few occasions where refineries are the better deal. It is usually more profitable and simpler to ignore them and use trade profits to buy resources on the black market (especially for TEC who can research a discount).

Get 1 (asteroids/dwarf)/2 (Everything else) population upgrades. Once you have money to invest, build logistical structures (Research, trade, culture etc). Then invest in more logistical slots, and build more logistical structures, until full.

All the other upgrades are situation. Planet Health and tactical slots are obviously only needed for planets in danger of attack. Exploration is usually a luxury for those with money to spare, but if you do get that huge economy why not.

Extractors! They're cheap, pay themselves off quickly, and don't use any planet slots. When first colonizing a planet the population upgrades and extractors are what you should always build right away without question.

Yeah, the TEC are all about lots of simple and efficient ships. The Advent and Vasari playstyles require more finesse and rely on using powerful abilities or research well, not as much on numbers and brute force.

You don't have enough fighters and bombers. Strikecraft are most deadly when you have a critical mass of dozens if not over 100 squadrons. Since strikecraft do not have collision detection (they can fly through each other), they can attack any single unit at once, while antifigter units (including other fighters) will have difficulty efficiently targeting that many units. While your strikecraft may eventually be destroyed if the enemy has lots of antifighter units or ships with abilities like Flak Burst, it is nearly impossible to protect key important capitalships, starbases or even titans from a properly executed bomber swarm.

Defense vessels aren't bad, but unfortunately they are mainly for fighters and corvettes. They do not do as well against bombers, which is what you usually fight more of late game since they can take out starbases.