Allow me to give you my recipe for domination over AE.I play as militarist,materialist,individualist,and military junta as government,thus giving me science,energy,damage,fleet upkeep and upgrade boost.This allow me to exceed fleet capacity without significant resource shortage,and have fleet that bigger,and more advanced that my neighbors have(unless its an SA).Its also important to have extreme adaptation trait,that gives you the ability to quickly expand borders and colonize all planets inside it(except tomb worlds)in early game without the nned or terraforming or genetic adaptation.When you colonize all "free space",just sit peacefully inside your empire,gathering resources,killing native alien fllets,and keep others fllet power as "inferior" compared to yours so nobody dare to declare war on you(aside from some crazy purifiers).And when the time comes,and by the time i mean crisis/awakening or both,you will have fleet of about 250-350k to welcome them.
Few words about fleets.I am using two types-corvette swarm and battleship line.A large swarm of corvettes(200-300)will just "eat alive" fallen empire fleets and leviathans while evading from most of its attacks.100 Batlleships with giga cannons,one KA,two bomber and one fighter squad wil just kill enemies from save distance(works best with the unbidden)