Welcome to the forums, by the way
Lightning turrets: I've done a lot of lightning turrets, they don't seem to do that much damage.
They actually do way more total damage than any other turret (with the possible exception of the heavy beam cannon, I forget), but they do very little for actually reducing enemy firepower by themselves, because basically nothing dies until it all dies at once.
Flak turrets: Are they decent AOE? I was turned off by the "bad vs armoured" thing.
They're pretty good, yes. Though right now they can get distracted by missile frigates (which they can hit directly but are immune to the aoe part) which can cause problems if the enemy frigates are separated from the non-aoe-immune enemies.
Riots IIs: Don't know them. Are they the designer starships?
The modular ones, yep