So almost a week after 0.6.0 launched and many captain respecs later. I've come to realize that only a couple of my initial builds have stood the test of repeated play.
Instead of going Ship by ship, I'm going to break this down a bit more generically.
NOTE: I choose priority target in the first row fairly often as I enjoy having the skill, but really any Tier 1 skill can be substituted.
Generic BB Build
This is the build I play on most battleships, especially the IJN line up to and including the Yamato. It combines survivability with Main Gun punch. It's important to note that I combine this build with Damage Control Modification 2, Aiming Systems Mod 1, and the Increased Main gun Rate of Fire mod (even on Yamato), when these mods are available. Additionally, I use the Fire flag to reduce fire times further.
Order of Purchase: Priority Target -> Expert Marksman -> Superintendent -> Manual Fire Control for Secondaries -> AFT -> Basics of Survivability -> Adrenaline Rush
This build is useful for Battleships focused on AA, like the North Carolina. Remember that for this build to be worthwhile, the DPS from the largest Caliber AA guns has to be reasonably high, as Manual AA Control only doubles the DPS of those guns.
I pair this build with AA Range Mod, AA, and fire Flags.
Order of Purchase: Priority Target -> Expert Marksman -> BFT -> AFT -> Manual Fire Control for AA Guns -> Basics of Survivability -> Adrenaline Rush
Generic Cruiser Build
This is the build that I'd use on most Cruisers, especially cruisers with 203mm guns. Note that if the cruiser does not have a fighter, use a different Tier 1 skill. Also, cruisers with repair party can choose Superintendent over BoS.
Order of Purchase: Direction Center for Catapult Aircraft -> Expert Marksman -> Demolition Expert -> Concealment Expert -> RPF -> Basics of Survivability -> Adrenaline Rush
150-155mm Cruiser Alternate Build
While the generic cruiser build is 100% viable for these cruisers, they benefit from inertial fuse for HE shells. This build is focused on killing BB's and high armor targets, so eschews RPF in favor of IFHE. Additionally, Adrenaline Rush is moved up in priority over Expert Marksman.
Order of Purchase: Direction Center for Catapult Aircraft -> Adrenaline Rush -> Demolition Expert -> Concealment Expert -> IFHE -> Basics of Survivability -> Expert Marksman
AA Cruiser Build
The AA cruiser is one best suited to division and competitive play when you KNOW there will be an enemy carrier. While it's still viable in normal random play, it knowingly sacrifices some versatility for maximum AA potential. Note that many cruisers carry the bulk of their AA fire power in the mid-range guns and therefore Manual AA is not as useful.
This build uses the AA range mod and AA flags when able.