Ok this is my idea so far
first: I think the vesta (as every other sci ship) gives its best on a sci character. However being itself a sci ship/escort hybrid it should be really nice on a tac too
This said, let's get deep into the build
the first thing I've noticed is you're using torpedoes. Forget that.
Torpedoes are useless on a ship like this and using them you have an awful loss of DPS.
So that's what you should be using:
Front: AUX DHCs x3
Rear: one phaser beam array and 2 tricobalt mine launchers
Lieutenant Tactical: Tactical Team 1/Cannon scatter volley 1
Lieutenant Engineering: Emergency power to shields 1/Auxiliary to structural 1
Ensign Universal (Science): Hazard Emitters 1
Commander Science: Transfer Shield strenght 1/Hazard emitters 2/Transfer Shield Strenght 3/Gravity well 3
Tactical consoles: 3x Phaser Relay; 1x TCD subspace infuser
Engineering consoles: 1x Monotanium alloy (protect you against kinetic dmg); 1x Neutronium/Electroceramic (the electroceramic gives plasma resistance)
Science consoles: the quantum phaser (if you want); assimilated module (even without the KCB is still a great console); 2x field generator or 1x field generator and 1x particle generator
Now please be careful: use the tricos in STFs or other PvE content only. PvP players define these mines broken (and tbh they ARE, I totally agree with them), as for the cluster torp, so I think if you want to be a fair pvp player give a look to the PvP setup.
Then the little beam array. If you're about to do a wide use of your heals the cmdr and ens universal slot you'll take advantage of your aux dhcs and put max auxiliary. This will give a huge boost to your heals and resistance skills but you'll do great damage as your cannons will be powered from aux
Then, the little beam array. You'll take advantage of that using your beam target to abilities when shooting at large targets like the tac cube on Infected: put your ship to the top of it, fire simultaneously trico mines, aux cannons and the beam with beam target shields. With some practice you'll be able to do nice damage (not like an escort but a lot more than any other cruiser/normal sci ship thanks both to the aux dhcs and your personal skills) but you will be able to tank alone the tac cube and keeping your teammates clear from these dirty plasma fires , and btw when you're doing khitomer, replace the peregrines with the danubes if you're going to take probes (yes you can with this ship with no worries).
here just replace the trico mines with chronitons (transphasic if you're doing 1vs1) and slot the proper dmg type console. Also, replace HE1 and TSS1 with Tractor beam 1 and polarize hull 1. Maybe you should ask an expert more hints about the consoles to use. Then give a read to this guide http://hilbertguide.com/ if you hadn't already done that.
Hope you'll begin enjoying the Vesta. I really love it on my sci betazoid