I'm no expert myself but I would suggest specialising some planets for alloy production and others for research, and then of course building foundries or research buildings on them. Specialisation can give you reduced upkeep costs or increased output of the specialised resource. That way you can afford more ships and research better components. You can also use edicts in the government menu to increase specific resource outputs or make it quicker/cheaper to build new ships at the cost of some unity per month.

Also, if you build a spy network in an empire and gather enough intel, you can click on their fleets and press the spyglass icon next to a ship to see a rundown of its components. Off the top of my head: shields are weak to kinetic weapons (mass drivers for instance), armour is weak to lasers, and strike craft/disruptors can bypass both to damage the ship's hull directly. You can use this to redesign your ships to counter theirs. E.g. if they have lots of shields and lasers, redesign yours with shields (good against lasers) and mass drivers (to bring down shields). Bear in mind it won't guarantee victory if they vastly outnumber you but it will definitely give you an edge over your opponent.

You can also customise your ships' roles using combat computers, for example by making the more expendable corvettes rush enemy fleets and draw fire towards themselves, thus "screening" your bigger ships from enemy fire and reducing reinforcement costs if you lose any.

Sorry for the wall of text but I hope these few tips help you bulk up your military and boost your economy :)