Federation Fleet
New Jersey class BCH Thunderchild - 220
2 x NCL - 320
1 x Texas class CL - 130
3 x Ramius class FFB - 330
25 photons, 8 drones (suited to defence), 40 phaser-1s forward
With this fleet the Thunderchild manoeuvres behind the rest of the fleet, so as not to limit them with it's Turn 6. This is not really important in the first couple of turns, as you'll be looking to close and unload those photons into the enemy fleet, but after the moment of decision and you having a couple of cripples on the board you'll be going to independent manoeuvering and the Thunderchild might find itself on it's own. Don't hesitate to trail the Thunderchild behind your fleet and jump a decently sized enemy ship with overloaded photons after they've traded punches with the bulk of your fleet. It would be the perfect time to slam a C7 in the side or to jump a BCH with damaged shields.
The main point of the fleet is that everything except the Thunderchild is Turn 4, which means that you can out turn a Federation gunline fleet and have some chance against Klingons. You'd be running what I term a heavy pack, Turn 4 cruisers and escorts packing a heavy alpha strike.
Or
New Jersey Class BCH - 220
Chicago Class NCA - 190
2 x Constitution Class CA - 360
Ortega Class DW - 120
Ramius class FFB - 110
24 photons, 9 drones, 38 phaser-1s.
Four big cruisers packing photons and 6-10 forward phaser-1s each with a couple of heavy escorts. One fewer ships, individually more survivable and gives you a heavier gunline. You could even trade the Ramius and Ortega for a second New Jersey (giving you more phaser-1s) or upgrade the Chicago to a New Jersey and drop the escorts to Burke class frigates (no overall change in firepower). This fleet is your standard Federation cruiser gunline.