Wow you guys sure don't build many destroyers! I always make my fleet up of like half destroyers, half battleships/cruisers/carriers, generally placing more emphasis on the number of carriers than battleships.
Early modern fleet: 4 Destroyers, 2 Carriers
Post-industrialism fleet: 5 Destroyers, 2 Battleships, 3 Carriers
Late modern fleet: 8 Destroyers, 4 Missile Cruisers, 4 Carriers
I find anything less than 6 fighters to be insufficient to bomb enemy ships before hitting them with mine... Likewise bombarding city defenders for the marines. 3 Carriers with their 9 accompanying fighters is really "the sweet spot" for a task force that acts independantly and is capable of suppressing enemy naval AND land defenses with minimal ship and troop losses. Fighters work great for naval combat, as long as you have enough of them to get through destroyer (and sometimes fighter) intercept chances. More carriers is IMO far more important than more battleships, as with sufficient air power you will be using your own destroyers to pick off their weakened battleships with ease. This is also why I build more destroyers-- they're cheap, disposable and start out with tons of movement points so you can build them en masse in marginal production cities. Whereas with transports, battleships, carriers you really want to be building them with at least 5 and preferably 10 xp so you can get them as many movement points as possible, which greatly increases your ability to wage quick coastal wars, nevermind successfully defend against suprise attacks.
I really hate using cruise missiles to be honest, it's too time consuming to be constantly moving missiles around and reloading the ships. The point of a modern navy is to project your power a long ways away from your own territory, and having to constantly send your big fighting ships back to home turf to rearm is, well, very counter-intuitive to that. I love putting nukes on them though, then my fighters can focus on enemy fighters and bombing strategic resources, leaving the nukes to clear cities for my marines. Or two-shot massive enemy naval stacks.
My advice is build more destroyers and carriers. With only 1 or 2 carriers per fleet, you're not usually able to plow through their destroyer and fighter screens in a single turn, which is what you need to do to pick off those capital ships before they disappear back into port or start causing collateral damage to your transports and carriers. By massing destroyers you also make it harder for their warships to even get a crack at your soft underbelly, the all important carriers and transports... If you were building lots of battleships instead of destroyers, you'll have a whole lot less of them to soak up the incoming attacks when you get too close to an enemy naval base, or stack of doom. Nevermind the fact that this also gives you very solid protection against enemy air power, freeing your fighters to support the ground campaign.