colonizing your 1st asteroid

Going back to your original question, you may need to start out strong with a large fleet and fleet research. Personally, i get 1 lab: hostility on small maps and harmony on medium and larger maps. You said that you are an economic player; the Advent does not have as strong as an economy as the TEC. Basically, rushing and quickly building up your fleet are your only options. For fleet composition, I start out with a Radiance and 10-20 disciples and rush (for VERY small maps). I get an asteroid, upgrade its population and get the extractors, and research shields and lasers. Meanwhile, I'm building maybe 5 more disciples, getting the drone hosts, and the progenitor. For myself, this method works pretty well on smaller maps.

PS: If you really don't know what to do, I suggest playing some smaller maps on easy or medium AIs to get a feel of how to rush and build up your fleet. Advent is NOT geared toward the economy.

Offensive early game as advent only works against players with skill significantly inferior to yours. While advent has cheap scouts / disciples, their extremely low damage to building translates to a fairly long period of time during which your opponent can adjust his strategy and fleet composition (that is, assuming he hasn't done so when your fleet is enroute...). This, in turn, makes early raids quite difficult for advent.

Playing against someone with similar skill level, it is probably better to scout constantly and go defensive (build counters!) until you can start massing illums/HC. As far as counters for early assaults go, advent got some of the cheapest and most effective units among the three factions (scouts, disciples, defenders), so you will likely be ok until the other side starts pumping HC.

Advent tends to have a hard time against vasari because of phase missles, and 1.03 makes mid/late game so much more favorable to TEC. I personally have doubts whether advent is a viable choice in a competitive game until 1.04 is out.

"Last night against AI I fought my Evacuator (L6 or 7) and assailants versus his Radainc e(L2) and disciples."

Especially combined with Malice. Malice and and the Halcyon's weapon rate of fire enhancement are both good by themselves. Together, they are hell on wheels.

I've won a game as Advent. The trick is to get a couple of capitals with strong special abilities (I don't go for Radiance until mid-game; Advent strength is in special abilities). It was a 2v2 set game and the two opponents ignored my partner and bull rushed me early; the Advent player's worst nightmare. However, through intelligent use of special abilities on my Mothership and Halcyon carrier, plus some micro managing of my bombers, I soundly wacked a mixed force of Advent and TEC opponents that outnumbered me at least 3 to 2. I didn't lose any capitals, but I popped an Akkan and a Radiance. Now, I did take heavy losses. They nuked two of my four colonies into the ground I took heavy fleet losses. But they gambled everything on beating me completely. Since they didn't, my partner sailed his fleet into their space completely unopposed, and they had nothing left which even had a chance of defeating him. For that matter, I had damaged them so severely that I don't think they could've even successfully contested my home system. When they came in, I started saving resources to build replacements for a counter attack.

Malice plus Halcyon's rate of fire increase is potent against the hordes of Disciples and Cobalts they sent after me. Also, my use of bomber squads combined with Malice was pretty much decisive. My bacon was saved by CVLs running bomber and fighter squads.

How bout some replays?