Vasari coming... at some point?

Build 1:
Standard 1v1 (non rush) build on small-medium map:
1.  Buy 2 units of crystal
2.  Upgrade home planet
3.  1 Worker on Cap ship, 1 worker on crystal
4.  Build 2 seekers, scout
5.  Start Radiance when cap ship fac finishes
6.  Start 2 metal extractors
7.  Build colony ship
8.  Take nearby asteroid (all maps have 1 nearby asteroid)
9.  While taking asteroid, scuttle capital ship factory
10. Build 2 military lab
11. Finish the asteroid, colonize it, upgrade so you don't bleed cash
12. Mine all asteroids, and add 2nd military lab
13. SCOUT THEIR HOME PLANET.  If they made light frigates, build disciples (research defense vessels in meantime).  KEEP SCOUT ON THEIR HOME PLANET.  Once LRM production starts (and it will) start defense vessel production.
14. Asteroid #2 should be cleared and ready for taking (there's almost always a second asteroid, if not, find a lightly defended terran or desert)
15. Take asteroid 2, build it up as before
16. Continue spamming defense vessels
17. You have 3 colonies, you can decide whether to take more or contest neutral extractors (I usually do neutrals)
18. Add additional military lab, start research to Guardians
19. Whichever colony is CLOSEST to opponent, should build at least 2 frigates factories
20. Depending on opponent unit composition, build Drone carrier (to counter heavier ships and caps with bombers), more defense vessels (LRMs), or Disciples (light frigates)
21. Your capital should be 4 or 5 now, continue pressuring
22.  Eventually tech up to a second capital ship (Mothership), and get the guardians, then eventually (very late), Crusaders if you can afford them.

Build 2:
Rush 1v1, small map
1. Buy 2 units of crystal
2.  Upgrade home planet
3.  1 Worker on Cap ship, 1 worker on crystal
4.  Build 2 seekers, scout
5.  Start Radiance when cap ship fac finishes
6.  Start 2 metal extractors
7.  Build 4 disciples, then a colony ship
8.  Start taking nearby asteroid(s)
9.  Scuttle Capital ship factory
10.  Add 2 military factories, continue pumping disciples
11.  When asteroids are cleared, pressure with disciples, aim for labs if possible.  Make sure to scout for lrms (assailants)
12.  Research drone carriers
13.  Spam drone carriers and hope to wipe out his army
14.  Continue production and take neutral extractors
15.  Hope to kill them before they can counter your drone carriers with enough flaks.  Micro fighter/bomber away from their flaks if possible.

Build 3:
Economy build, larger 1v1, medium large 2v2
1. Buy 2 units of crystal
2.  Upgrade home planet
3.  1 Worker on Cap ship, 1 worker on crystal
4.  Build 2 scout frigates, scout
5.  Start Mothership when cap ship fac finishes, go Shield regen first, then Malice, Malice, Regen, Malice, Regen
6.  Start 2 metal extractors
7.  Build colony ship
8.  Take nearby asteroid (all maps have 1 nearby asteroid)
9.  While taking asteroid, scuttle capital ship factory, pump some disciples (map dependent) for early game presence
10. Build 1 Civil lab at main
11. Finish the asteroid, colonize it, upgrade so you don't bleed cash
12. Mine all asteroids, and add 2nd and third civil lab
13. Start research on trade, and continue taking any planet within reach
14. Start placing trade ports as income allows, research ice or volcano depending on allegiance to home and mineral quality.
15. Deserts are a priority, you can support a ton of trade ports per desert planet
16. You're doing this with little to no units, because you expect the opponent can't get to you in time.  If they can, you shouldn't be doing this build anyway.
17. With spare slots, tech to tier 2, and scout out their army composition.  A safe build is to add defense vessels and static defense (Beam platforms).  Drone carriers hiding in back are a viable defensive strategy as well
18. Tech to a second capital ship if you can afford it (Radiance is a good choice), add Guardians to fleet mix
19. Add illuminators for dps ONLY if you absolutely cannot hit tier 5 tech (which is hard, but not impossible).  If you can hit tier 5, add crusaders.
20. Once you have crusader + guardian + defense, start your offensive.  Keep everything in your shield bubble to increase shield mitigation.  FF their weaker ships (or autoattack with illuminators).  You have no easy way of killing capital ships, but your radiance manaburn can deal with their special abilities.

General micro tips:
Flak/defense/sentinel frigates do poor dps, but have incredibly high hp for frigates.  Here are micro tips:

Target weak units first.  Disciples on heavy armor, crusaders on LRM, illuminators on... nothing (CHANGE THAT DAMAGE TYPE ALREADY)

Malice is an important feature in larger fights, but is worthless in small encounters.  Furthermore, the Mothership has horrible dps for a capital ship.  Remember to keep it in back so it doesn't randomly die (it's the speed of the space whale).  Manually cast all spells, otherwise you'll just waste them.

The strong point of advent is their nearly unstoppable mid/late game once their synergies start working together.  The major weakness is their abysmal early game, and requirement to have multiple capital ships to be effective in fleet combat.  Furthermore, the race as a whole is very weak against Vasari (due to shield pierce).