Usually when I go to war I have a few small scout fleets that I sacrifice to see which weapons they use and slightly adapt my own 'specialized' fleet to it. But the largest part of my navy consists out of a smaller fleets designed like this in this reddit post, found it a really helpful one, their offense is quite low, but in my current playthrough all civ's around me are missile based, so they are incredibly effective.
About fallen empires, there are 4 different kinds, and each of them have a different trigger before they start acting hostile against you. They also use late game tech, so it's best not to do anything to anger them in the initial stages of the game until you know which kind they are.
You can identify em by these titles: Ancients, Ascendancy, Continuum, Core Worlds, Fore Runners, Remnants, Home Worlds, Progenitors, Shards, Successor State.
Keepers of Knowledge - Fanatic Materialist - Limits the spread of technologies it considers to be dangerous. Researching Robots/Droids/Synths and Sentient AI techs will anger this personality.
Enigmatic Observers - Fanatic Xenophile - Enforces ethical treatment of all species. Enslaving/purging pops or legalizing these actions will anger this personality.
Holy Guardians - Fanatic Spiritualist - Defends systems which they consider to be holy. Colonizing planets with the Holy modifier or any Tomb world will anger this personality.
Militant Isolationists - Fanatic Xenophobe - Protects its borders from neighbouring species. Colonizing nearby systems will anger this personality.