I am breaking destroyers up a bit more than frigates, since I am quite busy IRL. I plan to do the destroyers, and then take a break from just going through all the ships for some other topics.
Anyway, destroyers are sort of like frigates in that they have small weapons. However, they are cruiser speed (or even slower, with the corax going the speed of a battlecruiser!) and have significantly increased signatures without increased tank. They are slow and fat compared to frigates, and will take much more damage from larger weapons. They can have trouble catching other ships, even larger ones. Their main advantage over frigates is increased damage and damage application.
A word on heating destroyer weapons - destroyers have tons of highslots. You can burn out your entire highslot rack in seconds. Be very careful when heating, especially on long cycle time weapons like artillery and light missiles.
Thrasher - For a long time, the thrasher, like the rifter, was the best destroyer by far. Unlike the rifter, it is still very strong. It comes in a few variations, including shield autocannon, armor autocannon, 10mn ab with arty, kitingish with arty, and a FW version called a cockbag, where you basically just try to suicide gank in lowsec. With the short range of autocannons, and the high tracking bonus, you generally just want to ram things with the following fit. Against things that are higher dps and higher tracking, such as catalysts, staying at barrage range is going to be a wise choice. One of my favorite ways to modify the fit below is dropping a gun for a 2nd neut. Dropping the DCU for a 2nd gyro or the neut for a rocket launcher is also possible, and gives you close to 400 dps. Due to the lack of a web or afterburner, its still possible (albeit difficult) for ships to get under your guns. In those situations, heat the neut and hope they cap out soon.
[Thrasher, Shield gank]
Damage Control II
Gyrostabilizer II
Limited 1MN Microwarpdrive I
Medium Shield Extender II
Faint Epsilon Warp Scrambler I
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
200mm AutoCannon II, Republic Fleet EMP S
Small Unstable Power Fluctuator I
Small Projectile Ambit Extension I
Small Projectile Ambit Extension I
Small Projectile Collision Accelerator I
Talwar - Despite being slightly slower than the thrasher, the talwar makes for a much better kiter. The mwd sig reduction bonus is one of the most powerful bonuses in the game. It makes for a decent LML kiting ship, and is often found in large, low skill point blobs. The talwar bonused to explosive damage, which is somewhat rare for a missile ship. Because of this, you can have problems engaging t1 shield tankers and t2 amarr armor tankers. Carry EM or thermal rockets for these situations. Below I have given a fits for both close range, and kiting talwars. The kiting fit needs a t1 power core and a 3% electronics (ee-603) implant to fit.
[Talwar, Brawler AAR]
Ballistic Control System II
Small Ancillary Armor Repairer, Nanite Repair Paste
Damage Control II
Limited 1MN Microwarpdrive I
Faint Epsilon Warp Scrambler I
Fleeting Propulsion Inhibitor I
Rocket Launcher II, Caldari Navy Nova Rocket
Rocket Launcher II, Caldari Navy Nova Rocket
Rocket Launcher II, Caldari Navy Nova Rocket
Rocket Launcher II, Caldari Navy Nova Rocket
Rocket Launcher II, Caldari Navy Nova Rocket
Rocket Launcher II, Caldari Navy Nova Rocket
Rocket Launcher II, Caldari Navy Nova Rocket
Small Auxiliary Nano Pump I
Small Auxiliary Nano Pump I
Small Warhead Calefaction Catalyst I
[Talwar, LML]
Internal Force Field Array I
Micro Auxiliary Power Core I
Nanofiber Internal Structure II
Limited 1MN Microwarpdrive I
Medium F-S9 Regolith Shield Induction
Warp Disruptor II
Light Missile Launcher II, Caldari Navy Nova Light Missile
Light Missile Launcher II, Caldari Navy Nova Light Missile
Light Missile Launcher II, Caldari Navy Nova Light Missile
Light Missile Launcher II, Caldari Navy Nova Light Missile
Light Missile Launcher II, Caldari Navy Nova Light Missile
Light Missile Launcher II, Caldari Navy Nova Light Missile
Light Missile Launcher II, Caldari Navy Nova Light Missile
Small Ancillary Current Router I
Small Polycarbon Engine Housing I
Small Bay Loading Accelerator I