Unfortunately, the attack priority is given to those with the highest weapon to defense ratio [Off / (Def+HP)], so with your carrier group, they will always blow your fighters to smitherines first (because they have no defense and low HP). Then, if your carrier had no weapons, it's just a sitting duck waiting for death (even if it has insane defense lucky hits will still kill it).
Fleets of tiny hulls are best used around a military base.
Fleets of small hulls are best used around a military base.
Medium hulls are best used alone as defenders if you have a military base.
Fleets of large hulls are good battleship on their own.
Huge hulls are just bigger large hulls... nice, but not comepletely necessary.
As for a fleet's offense and defense, assuming you are not using military bases (and have the tech required), make multiple types of ships which focus on different weapons (IE: a fleet of 3 large ships should have one focusing on missile, one on beams, and one on guns). All three ships should focus into 1 defense type (the primary weapon that your enemy is using), and exactly 1 point of defense in the other two fields (so if your enemy is using lasers, make your ships have 5 shields, 1 PD, and 1 armor).
With the above fleet design, your enemy will never have a chance. They will literally never be able to adapt their defense to your weapon strategy, and even if they adapt their own weapons to your defense, and somehow managed to catch you off guard, they are still at a significant disadvantage.
But if you REALLY want an ultimate strategy, wait until you fight a few battle with this strategy. When you get one of your ships more damaged than the others, upgrade it to a design with a TON of defense, just make sure that its [off / (def + current HP)] is more than the next guy (which should be easy because in a few battles those ships will have leveled up some), and he will tank the enemy for the entire game. If you do this right, the game is just plain easy.