ACC would probably be the better option for beams. Followed by CritD or CritH.
I'd say stick with phasers for the proc. If you want to eat through shields, I suggest putting points into Flow Capcitors and getting a 2-set bonus from Omega Force space set (to get the Tetryon Glider passive ability).
If you what is called "Shield Stripper Build" Then go with Tetryon, with as much [Acc] as you can get. The more times you hit them, the more times the proc will go off. Also 2-piece Omega set, plus tachyon beam, and you will drop shields.
Default full power to shields since if my shields go down I'm toast.
You always want to run full weapons. During a battle you might want to switch to full shields, aux, or engines, but as a rule (for me at least) you are always going to want full power to weapons.
For you it should be about 120.
Your boffs are what keep your shields up, not your shield power(Well it does, but it should be your boffs that keep your shield power up high). For your eng boffs, use Emergency Power to Shields 1 and 2, and that will keep your shield power up.