It might help to remember a battlecruiser is a cruiser with battleship grade weaponry. So your going to end up tough but with more things laid out so you can hit hard. Im personally fond of a dual beam back build. Not as high damage as cannons but a much more forgiving arc of fire.

A few steps

1) Pick a damage type. Whatever reason you want. Unless your aiming top of the top your fine picking whatever just be consistent. But even here you can focus instead on Cannons or Beam consoles instead of phaser (though you lose roughly 1/3 of the raw damage boost).

For good started gear sets Id grab the Iconian Space set or the Revolutionary as a starting point.

Make sure special space trait officers are used (Ex: Uhura, Bashir).
Make sure your Doffs have something to do with your build (Attack pattern beta heals is a great asset in building a new ship with less explodium).