Well, I shall give my 2 cents advice on this thread.
I'm not used to the all x approach since I find it "unrealistic" (as how "real" future may be), but I shall try it one day, to be a score blockbuster too

but I'm off topic doing so ^^
But as far the thread is about, its about weaponery.
I play in huge/immense maps, masochistic, abundant all but habitable planets (common or rare) and tech slow or slower.
So... How to crush aliens in a few lessons..
First of all, Diplo is your friend: Early on, as soon as the first warships are being built by everyone, check AI's ships in their list in the diplo screen - assuming you got contacts with them and universal translator. Cheap spying, but still effiency. You can see toward wich kind of weap a given AI is going to focus on. Often beams weaps, sometimes mass drivers. Korath, Yor and Drengin seems to pretty like missile weaps instead, but not always.
So having in mind wich weapon kind your potential foe is gonna research, you can research appropriate defenses.
Early on, focusing on missile weaps will allow you to get expensive ships, but AI seems not research any ECM tech until you aren't at war with them AND using missiles against them. As for shields and armor, they often research for it due to early (often useless) wars.
Secondo, never ever trade (I mean give to the AI) +x% weaps and/or def techs giving bonus. As for diplo techs, it may turn one day against you. On the other hand, try to grab every unique techs aliens may have discovered in such fields.
Needless to say, try to grab those precious military ressources asap. It helps you show stronger to them (even if you got a "fake" spaceship power), since it grants you both weap/def bonuses.
Tertio: Ship designing is the key to victory. To only rely to core designed ships is (imo) a real mistake (you hadn't the choice in gal civ I, but now you do). One may say that core designed ships are a little bit better than player's designed ships (since they do have usually one or 2 "free" functionnal component aboard) BUT sadly they doesn't really reflect your real tech level: you might have very good shields but poor armor, then not being able to "discover" a kind of ship. Those ships often focus to a given weap and def kind: mass driver with armor, ect... Sadly, ie AI may have armor too and is using beam weaps. So that ship would be next to useless against them..
So don't be affraid to spend time in ship designing (and, like chess, it can be different from one game to another), it will be your key to military success.
Also, as said above, AI may seems VERY strong. But is is often a "paper strength". A good ship design, and bye bye AI's ships. Medium hulled size (or bigger) are better here, since you can fit on those the punch you need (the one AI cant defend since they don't have yet researched required techs) and some defense in the right field.
There is many schools about ship designing (you can design all attack ships without any defense aboard, or defensive ships with a few weaps, depending of your gamestyle and how strong your foe is, practise is your buddy.), I won't get into that topic here otherwise my wall of text already here will be a galaxy's arm sized wall of text

Here is enough for now, don't hesitate to ask questions, we are all here to help.
Edit: Forgot to say that miniaturisation is your friend: it means more things on a given hull size, like an additionnal engine, life support, fleet module, ect... However, check how many same components you use on a given ship: sometimes the best "miniaturisation" is to research the next step in weap/def/engine/life support tech than "global" miniaturisation, especially for all weapons ships.