Pair transphasic with plasma rather than tetryon. Transphasic does hull damage, as mentioned earlier, even while shields are up. The plasma fire of plasma beams will compliment this better than tetryon. Transphasic are great in PVP for going through Reverse Shield Polarity. I still fly with plasma beams and transphasics, but I'm considering a respec with the RSP nerf.
Plasma beams arn't so common in PVP because most people use hazard emitters, thus no real benefit to the proc. But if you play mostly PVE then you will get a lot of extra hull damage from the plasma fire / transphasic combination. This is really nice for when a sliver of shield regenerates to prevent full torpedo damage on the hull. As a side note, if you have the automated defense turret then it also benefits from plasma consoles.
If you really want to focus on bringing shields down then go with tetryon (and rapid fire if you use cannons)paired with photons or quantums. Photons are best if you autofire, and Quantums are best if you are a "select your moment" guy. Also, Quantums will make more of a torpedo high yield 3.
If points are tight then use phasers rather than tetryon. Most people do these days. Not only are they cheaper but the occasional system shutdowns, while random, create real opportunities for success. Furthermore, high phasers (or disruptors if klingon) will enhance the skill of your support ships as well. At Admiral, everyone gets NPC reinforcement and these ships use the racial weapon of choice.
Science Admirals tend to use phasers (or disruptors if klingon) because their photonic fleet benefits from this skill as well. Given how tight points can be in science, this makes phasers a must.

So from your description, I would say that phasers or tetryon are good (for shields). Use lots of rapid fire, and go quantums with the torps. But use plasma with transphasic for PVE hull damage.
Personally, I'm not big on putting mines on anything, but least of all on an escort. But I have seen a few people doubling transphasic torps with the breen mines as a rear firing weapon for pass by attacks. It depends on how much power you need to save, and how many skill points you have for mines.