Personally, with STFs in mind, I use DBB, DHCx2, quantum in front, and turret x2 and tricobalt in the rear. The DBB with beam overload can strip a shield facing, and followed by high yield can be lethal. The tricobalt is for whatever survives that or to get a massive hit on unshielded structures in STFs or clearing out a wave of fighters on that carrier in The Cure.
Stick to one energy type. The only benefit of having different types is that you can get different procs, but the tactical consoles you'd need in that case give lower buffs than type specific ones, so you have a significantly lower DPS right out of the gate. Having different procs is counterbalanced by diluting all of their proc rates.
As for the quads, only if you're using the matching energy type obviously (I use antiprotons, so never even considered them), but they're kind of a questionable pick. The engine hit isn't so bad in an STF like it would be in PVP, but the benefits are still questionable.
if you really must use the quads, then phasers- phaser relay console takes full advantage of that weapon type, so itd be a bad idea not to.
as for loadout, everyone has their opinions. i use 2 DHC, 1 quantum torp, and 1 DBB up front with x3 turrets in the back- every now and again i may use x3 beam arrays just for fun. if you dont have beam overload 3, its probably best to use 3 DHC front, but its really a personal playing choice. I use AP weapons on one toon and polarons on another- some use phasers, others disruptors. its really all up to your play style, what you like, and what your doing.