As Darvin said for Advent (mostly) and Vasari they're colonizers ARE the most powerful and if a vasari takes ANYTHING but the space egg then something is very,very wrong with them. Normal and hard AI don't prove much since they only spam light frigates for first 15 min or so and build random caps.
This is what i do.
1.Build cap ship factory que colonizer cap or Marza fo TEC.
2. Scout 2-4 depending on map, location etc
3.Upgrade planet population.
4.If Vasari mil lab for assilants, If advent 2 mil labs (1 first then 1 more in like 2 min) for carriers. If TEC 2 for LRMS (THIS IS ASSUMING THAT YOU HAVE AT LEAST 1 ROID TO Start
4b. if no roids then 2 civic labs for ice/volcano
5. Send cap out to colonize roid (NO LIGHT FRIGATES)
6. First i coloinze roid forget the stupid militia ships after its colonized kill the seige (it doesn't have enough time to kill planet.)
7.Upgrade build extractors etc.
8. Research carriers or long range frigates (LRM.Assilant for VAs/TEC) Carrier for Advent.
9. you have 2 choices continue researching and get rep platform for when cap needs to take terrans or deserts or start up LRM/assailant/carrier production
If your in the pocket then i go Eco and do everything above except subsitute all mil research with civ research. This works great for me but all of this has to be done fast and there is some selling and buying of resources on the market but i forget how much and what. This is what most players do but how fast you do it and how you can evaluate what you need where you are is what is important.
Edit Sorry if this is hard to read if it is unclear what i mean i will edit it or some grammar nazi will correct for me.