Energy weapons deal damage to the opponents shields very effectively but are not good against the hull. You will use these weapons most to knock out opponents shields and to keep them down.
For an Escort, you want to use energy weapons with small arcs if you're running a fast an agile ship. Your agility will make it such that you can use weapons with small arcs (45-90 degrees) more effectively since you will be able to reposition that arc against the enemy more easily than a cruiser could. In addition, weapons with smaller arcs have higher DPS.
- Dual Cannons have a 45-degree arc and some of the highest damage output of any weapon type.
- Dual Heavy Cannons do about the same DPS as Dual Cannons. However, the fire slower and do more damage per volley.
- Quad Cannons, similarly, fire slowly and do more damage per shot.
Which of the three you use should really be a factor of how far you can get from the enemy before you start your strafing run. You'll want to choose one that is such that you're last volley fires right before the enemy leaves your firing arc. If you can time runs such that you get that last shot off before you have to veer with a Quad Cannon, you'll be the most effective. Aside from that, make sure you're using the strongest Mark type that you can afford/obtain/equip.
You should try to avoid anything else. If you absolutely have to dive into other weapon types for some reason, Dual Beam Banks are not a terrible fallback when you don't have access to Dual Cannons or better. Choose Cannons over Beam Arrays, and Turrets last.
Torpedoes do not fare well against ship shields but they are essential to damaging a ship's hull effectively.
Torpedos only come in one type of firing arc (90 degrees). Mainly, you need to make sure to have some torpedo batteries on your ship to quickly kill an opponent once you've demolished their shields. If you try to stick to all energy weapons, your DPS will drop once their shields are down.
Again, make sure you're using the strongest Mark type that you can afford/obtain/equip.