While I agree with Darvin, a typical fleet (fighting against your typical Insane AI) would be something like this:
2x Radiance
1x Halcyon
1x Progenitor
10 Scouts
25 Disciple
50 Illuminators
25 Destras
15 Iconis Guardians
15 Domina Subjugators
25 Defence Vessels
5x Aeria Drone Hosts
As you can see, the Illuminators are pretty much the mainstay of my fleet, thanks to their large firing arcs (front and the two sides). I use a combination of Fighters and Defence vessels to take out enemy fighters and protect my own ships, however don't tend to waste the resources on building up a massive fighter fleet of my own (the Advent get a fair few fighters as is anyway), as any developed player will know better than to send a fleet in without their own fighter cover. The Destras are there for heavy backup, the Disciples to remove any enemy carriers, and also deplete enemy cap ship antimatter. Scouts are there for mine-sweeping, or if things go badly wrong, suicide runs. The Guardians/Subjugators are there to repair your ships, and sometimes to suppress enemy ships (however own ship survivability is the priority). My cap ships tend to move together within the fleet, so we have two Radiances for insane firepower support, a progenitor to keep the cap shields up, and also a Halcyon so that even if the defence vessels/ Drone Hosts die, I have some fighter cover.
And once I've cleared the enemy planet of defenders, a bunch of Siege ships jumps in and finishes the job. The progenitor then colonises, I build a repair platform to fix up the last of my wounded ships, and off I go to the next system.