If I may so be inclined to say that my Independence class LCS has the capability of ASW by having the ability to ferry 1-2 ASW Continuous Trail Unmanned Vessel (ACTUV). Which are actually kind of cool, they are unmanned drones that actively seek and follow enemy subs. Sadly they do not engage the enemy subs but they do transmit data back to the LCS, which we can deploy various countermeasures from the knowledge obtained.
As for a DDG I was looking at the USS Zumwalt but I decided to go for more of a multirole vessel such as the Independace class LCS. :)
I cant do anything about AAW; however since you are manning a CVN I can only assume your fighters can make short work of anything on the surface.
[hider=P.S.] The Comanches aren't necessary on my LCS but they are there for my personal satisfaction of naval stealth helicopters. I can exchange them for more needed vessels if required. [/hider]

EDIT: I forgot to add the ACTUV to the list of vehicles on-board as I forgot about it and I wasnt thinking about the tactical aspect of it, I guess I was in complete bliss of the fact i could be in command of a crew aboard the Independence class LCS. So yeah I can make changes if needed. Just let me know as its quite the adaptable vessel. :D