All you need are cap ships heavy cruisers and defense vessels.Try 4:1 heavy cruisers to defense vessels with as many cap ships as possible.The only thing that can counter your heavy cruisers are bombers which get torn to shreds before doing much of anything by a pittance of defense vessels, and heavy cruisers which you can out micro or out spam. A few shield support vessels are also useful.
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I would make a similar fleet but substitute Illuminators for the heavy cruisers. I think they are far more effective for the cost and the first thing they will do without even being
ordered to is kill the cap ships which can cause at least computer players to retreat. Now I just need Guardians with them and some support of their own and I can pick off ships at will as the Guardians disperse them all over the place. Other advantage is Illuminators are faster than all of the ships in the above mentions fleet and don't have to turn to be effective. Good range and with the Guardian push ability can be kept fairly safe.
Even if they get dispersed by enemy Guardians the recovery is faster and they won't have to turn to keep shooting everything in range... which is sizable.
I agree with italia559... experiment with a Illuminators also. Weak alone...massed they are wrong. Better for the cost than Advent heavy cruisers which have up to now failed to amuse me.
Also except in very long games you just won't be able to field all that many Capitol ships... the research is expensive and you will be over run long before you can get them going at... least vs. a human enemy. With a computer enemy it may be easier.