I suggest getting 3 hostility labs and researching drain antimatter. Then you make nothing but disciples! You will die of course, but the soudn they make is so precious!
Actually, getting drain anti-matter and illuminators is a good combo. Illuminators are great firepower, and disciples make excellent support, disabling anti-matter abilities that can give illuminators a hard time. Great against carriers, and really gives Advent a nice alternative to just rushing to get their own fighters out to counter enemy fighters. Doesnt hurt that you're well on your way to repulsion, either...
Oh, and Holy Trinity = Progenitor Mothership, Radiance Battleship, Rapture Battlecruiser. Read their abilities, think of how they can mesh together, and you can see for yourself what kind of destruction this trio can wreak upon their enemies.
You'll probably want to bring out the Halcyon and Revelation as well. Advent are probably the only faction where your first five caps are likely to be one of each. They each bring something very unique and useful to the fleet overall.