advent strategy is generally outlasting other fleets. you can have a comparatively small armada, and take out a army twice the size of yours. the trick is to know their synergies. the battleball is a good defensive synergy (guardians with illums and progen) along with your trinity (progen, radiance, and rapture or halcyon). Basically the good way to go about starting a game with advent is:
1. ALWAYS get the Progen as first cap (one of the best caps in the game if you ask me)
2. Build 3-4 scouts and scout the map
3. Build about 5 disciples
4. Head to first asteroid with cap and capture it.
5. Start building 3 temples of hostility.
6. Get your illums
7. Get your guardians
8. When you've got about 3-4 illums and at least one guardian, head to the next big planet that has more rebel groups.
9. Make progen fleet commander, and make a tight fleet formation with cap, illums, guardians
10. Head to next planet and make use of your guardian and regeneration abilities.
11. Watch, then, if you keep adding illums, guardians, a radiance, and a rapture and halcyon, you'll loose very few ships throughout the rest of the game.
that generally how i start and it works effectively. hope it helps