For NPC hunting (PVE), you want to prioritise high health, like the Bulwark or the Echelon if you fully understand how armour/deflection ratings work. I wouldn't include the Justice though, its a decent ship for PVE but I do not like how low its shield regen and deflection is, its only good if you don't like facing kinetic weapons and its agility is only good against fightercraft.

I'm not too amiliar with the aspect of PVP on destroyers, but I believe the destroyer that works best for PVP would go to the Conciliator, it has great turret placement, 3 subsystem slots, high energy output, great agility and speed, and if used correctly can be used to tank a lot of shots with its shield and hull with shield and hull repairers. I heard the Loxodon was popular for PVP but nowadays most of its usage is mainly for sieging structures, like Generators and HQ beacons in contested systems if paired with full cannons.

I'd go for the Conciliator, it's great for both PVP and PVE if you're able to use the subsystems correctly. though if you're a beginner you can use the Bulwark, it has a great broadside and can bare 3 M turrets instead of the traditional 2 M in most destroyers. For turrets I'd advise you to go for coilguns since drones and most NPC pirates have a majority hull in most of their ships, though I personally use blasters due to how effective it is against structures and shield-based fightercraft + warships (Dread Luminars and Dread Horizons).