Paragon for all-round combat, Onslaught for fire support, Astral for saturation support, and Odyssey for general purpose.
For flagship favorite capital, I am tied between Odyssey and Astral.
For the Odyssey, I use dual autopulse on one side and Guardian PD on the other, using expanded mag and auxiliary thrusters hullmods to go yippie-kai-yay flanking an enemy ship with the plasma burn while other ships maintain the battle line. The autopulse is supported with 2 ion cannons and 2 IR pulse lasers for sustained fire while the autopulse charges, but needs to be closer for it to work.
For the Astral, I focus on giving out commands and deploying fighter or bomber screens depending on the outfit. They are normally all 6 of the same type to perform specific roles.
Though my usual command flagship is the Doom phase ship, providing key strikes that turn the tide of battle. Due to sseth's video, I gave the phase cruiser the Stand autofit designation in honor of his contribution to the game's visibility. Yes, Doom is my Stand, and making enemy fighters explode next to intended targets is what it does, and its antimatter blaster and reaper combo gives no slack.