With the exception of very small maps where the enemy is only 2 jumps away you sooner or later will need need at least a few civic labs anyway so building one right on your capital does not hurt. Always research the terran planet population upgrade (if your capital is a terran).
It is cheap and will easily pay itself off within mere minutes.
You dont have to delay colonisation because of it. Just use LF instead of corvettes for your first expansion fleet and later bolster/replace them with your normal fleet.
One thing many people fail to recognize is that economy does scale exponentially in the early stages of the game. Because having more money means lower delay between colonizing and developing planets which in turn means that they will generate more money a lot earlier than those of your enemies.
Also dont ignore the extractor upgrades.... the increase might seem pathetic at first but again, consider the effect over time. In 4 minutes it will make a notable difference.
Now, of course you should not sacrifice fleet for such upgrades... but realistically... there is often an opportunity to fit one of those upgrades in.
For example, you shipyards are already building 10 ships in the queue..... instead of adding ships 11 and 12... resarch ressource upgrades. By the time the queue has hit 2 ships you will have more than enough money to queue up again... so continous production is not affected.
If you cant in early game, make sure that unless you are currently fighting for your very life that you get those upgrades, too.
I saw more than one replay where people are struggling to replace their losses in time..... having 30 % more ressources does help a lot.
Trade while being all powerful can only compensate so much, especially for Advent.
Your Credit to ressource ratio is at best 4.5 and at worst 6.0.
So for every 100 crystal extracted you just saved yourself 500 credits.
Global Unity can be interesting... 10 % more total income is nothing to sneeze at at larger empires.... and assuming you somehow manage to have 8 harmony labs, Allure of the unity can lead to 20 % total income increase..... Advent Rebels may have the Eradica but when it comes to economy... the Advent Loyalists are superior..... which actually suits their theme as being late game juggernauts.
Should I focus on metall or crystal?
The Vasari have an advantage here... they gain both with one resarch. For TEC or Advent it is situational, but unless you have a vulcan or ice planet at your disposal, you should probably start with crystal. Metall is not only easier to come by but as a result is far more rarely bought on the black market, leading to far better prices.
Again, most economic resarches should be done if you have currently ressources to spare. That means either all yards have a nice queue or your fleet capacity limit is reached.
Dont fleet up to early, unless absolutly necessary. If you intend to rush the nearest enemy, feel free to ignore any and all eco upgrades for corvette spam.
Notice however, that should your rush fail, you will be at a considerable disadvantage and quite helpless against a counter strike until your fleet is rebuild. If your rush failed against somebody who put a litte bit more effort in his eco, you can no longer hope to win a war of attrition.
This is why some people cry so loud about Wail..... it ruins their "I build 60 corvettes win button." and boy, you dont want to replace that fleet with a poor eco.