As others stated any light cruiser or below are good. I also go with an ASW/GUNS combination with my destroyers else your useless once the submarines are gone. Also is rather an waste to use your premium hedgehogs upon submarines that are surfaced and crippled, when you can just end them with guns.
Although as the single hedgehog salvo upon the T's does not tend to sink most submarines your aim within battle tends to be more about shadowing the enemy submarines keeping them sighted so other ships can avoid and engage whilst you continue to take pot shots with the hedgehogs.
With the depth charges though, when you drop them that submarines buggered. Although you need to get on him, and when you cant close that quick your just going to have to shadow him and again keep him sighted, but without being able to take those pot shots as you would with the hedgehogs.
L's are probrably the best choice, get the advantages that comes with the higher level ship. More speed and displacement to use up upon armour, weapons and keeping your crews as topped up as possible. Just having three R mounts is probrably the sole disadvantage although that mainly affects what you do once the submarines are gone, and the guns are given more space so they can be higher level guns or have more ammunition though to compensate this.
Tribals are well, sorta slow and have rather large beam. So not very good to use with depth charges where you need the speed to get close. Sole advantage I would say is that the L's weakness is the Tribals strength, there are four R mounts and with good space so is better with the "what to do once the submarines gone".
Q's are nice and pack an good anti-submarine punch due to the two T mountings compared to the single mounting the other destroyers get in NavyField. Uses the ammuniton up quicker though obviously when not shooting with gradual.
O's alright, nothing terrible, not much shockingly amazing either. Just an good ship.