Capitals: 1 Radiance, 1 Progen, and 1 Rapture
Not in that order, I hope. Radiance is a poor choice for first capital ship. Typically you should either pick Progenitor or Halcyon as your first capital ship as Advent. Sometimes you need a Progen or Halcyon, but after the first pick you generally can't go too wrong with picking caps as Advent. They're all pretty solid.
If your opponent has lots of strike craft, or your fleet starts getting very large, you should seriously consider the Halcyon. Its telekinetic push ability lets it swat away strike craft with ease, and its energy amplification aura increases the damage of all nearby frigates, making it invaluable to a late-game Advent fleet. Early game, its Adept Drone Anima ability gives it more punch in combat by giving it additional squads.
How is this fleet could it be improved?
Typically you either go all destra or all illuminator; 50/50 really doesn't work out all that well. You should also be working in the guardian support cruiser. He can protect your entire fleet and make them take reduced damage. Combine this with your Progenitor to restore shields and you've got a monsterously powerful fleet at your disposal (this is commonly called the "battleball", as Advent players will bunch up all their units into a tight ball to fit into the guardian's special effect radius). If you go with illuminators rather than destras, you can use the "repulse" ability to literally push enemy units away from your fleet. Only units that outrange the illuminator will be able to attack you, which is very useful.