ohohoh, a Vesta thread, I gotta comment (lol, yeah I noticed I pop in these up ).
check my signiture for full on builds for the vesta.
for pve here are some tips (they would translate to pvp, but as I cant give sound advice on pvp due to the lack of tests, here is this disclaimer)
generally the build is not good. decide what you want. beams, or DHC. the two wont go hand in hand. you can go full with the aux DHCs (you can dismiss and reclaim your ship so you gain 3 aux DHCs if you did not buy all three ship models).
I suggest losing the torps, the Vesta with 6 weapons does not concern itself with weapon drain. use either dhcs (or aux dhcs) plus turrets (same type ofc, and populate the tac slots with the relating tac consoles).
console wise apart from the obvious upgrades, you should get three universal consoles (they are not cheap, but they are the basis of every good ship build so they are worth getting): tachyokinetic converter, assimilated module (on a dhc vesta you can get the kinetic cutting beam next to it, though on a beam version it would not make much difference), zero point quantum chamber.
for ship engine and deflector get the borg ones, and for shield use the maco ones (again a basic setup, you can mix this up if you want, tho this is a working combo).
skill wise I suggest using sci and eng teams, and getting another tac team. use grav well 3 (and maybe next to it a GW1 too for the shorter cooldown). lose the tractor beam repulsors 99% of the time they are just annoying, and most of the time a gw can do the same job. get transfer shield strength, and reverse shield polarity. and you might want an attack pattern too (I like omega better, but beta boosts your pet dmg nicely)