As Aristotle once taught Alexander the great: Every situation is different.
It is possible to get no civic labs at all if and only if you can acquire 5 planets without the civic tech research. I still manage to have the #1 economy in a lot of these games. The economic (civic) research actually doesn't net you much of a boom to your economy... maybe 10-20%. Whereas, increasing your population caps on your planets and building more mines nets you much more percentage wise until you have around 5 or 6 planets.
Now, of course, if you're building 2 civic labs anyway you might as well upgrade a couple of the things there. I usually get the phase lane warning research and the 2 upgrades to terran pop cap first since they're cheap and well... you get 80% of your credit income from your home world which is, well, a terran planet.
I typically don't get more than 2 civic labs until I have 4-6 planets. When you only have 3 planets, it's much more worth while to capture another planet than to get trade posts. Trade posts are very expensive and take 5+ minutes to make up for their cost, and even then only when your planets are relatively spread out.
My advice: You're playing vasari. Against human players you need to be getting a ton of assailants or sentinels early (Otherwise other assailant / lrm / even drone host armadas will steam role you). Focus on getting a lot of planets and a lot of ships as early as possible. Upgrade to the max planet population capacity as soon as possible on every planet you take. This is what makes your economy improve. Negative credit income from undeveloped planets is the reason why most players have shitty economies (upgrade this as soon as you take the planet, no later).
Once you have a reprieve from the fight (ie: your opponent has a larger fleet than you so its not worth attacking or you are teching or you are playing a large game and have an extra 5 minutes to waist making no ships) Make an extra few civic labs and upgrade to trade ports. Upgrade the culture building and build one by your home planet to get it to 110% loyalty (that'll more than make up for the cost of one of these buildings). Secondly, build trade ports starting with your planets furthest away from eachother (that'll maximize your trade income while youre still building other trade ports).
Once you have those things upgrade the first tier of crystal/metal extractor rate things.
After all that you should have a sufficient economy to go for dark fleet or tech up heavy cruisers / whatever you need.
Remember: always have a large enough fleet to repel any attack.. too often players get their asses kicked because they go for an "econo boom" strategy. This is the hardest type of strategy to use effectively because you need a huge investment to make it worth while. My advice: just keep a large fleet and build up economy later.
Vasari are not any worse than advent or even tec as far as trade ports / culture labs. The tec can get these things earlier, but you don't want to make an investment in trade posts this early anyway or you'll be steam rolled (At least, I would steam roll you in even a medium sized map). Now, very late game the vasari do have a slight disadvantage in that they don't have rediculous trade upgrades like the tec do, but you have dark fleet! go dark fleet if the game is lasting that long!
So a build order:
1 Millitary Lab
Assailant Prototype
Pop Civic Upgrades on All Acquired Planets ASAP
If you need to take ice/volcanic planets to get 5 worlds:
2 Civic Labs
Planet Req Research for Ice/Volcanic
Terran Planet Cap Upgrades
Phase Space Monitoring
Get a ton of assailants and attack (keep you opponent on the defensive if you want to win)
other ways to win: just get 5 planets then go for an "econo-boom" strategy if and only if you see your opponent is not intending to attack. Otherwise you'd better attack. After econo boom (ie: making trade ports at all planets) go for millitary labs and get heavy cruisers. In my oppinion this is only worth it if your opponent has a ton of defense vessels / flak frigates / sentinels.
I am an aggressive player and attacking >>>>> defending.
At the very least you need to raid your opponent.
In a game where once you lose your fleet you lose the game, the idea is to destroy your opponents fleet.. Focusing on anything else will result in losing your own.