All the classes with their perks I've found, so you can decide which Responder is right for you.
2.Baseball rookie* - more stagger damage from two-handed melee attacks
3.Bear hunter - heavy rifles penetrate more targets
4.Courier** - increased backpack capacity (+2)
5.Deer hunter* - reduced noise from movement
6.Deputy - shotgun pellets have reduced spread
7.Designated marksman - heavy rifles deal increased damage
8.Detective - handguns deal increased headshot damage
9.Engineer - greater lifespan for flashlight batteries
10.Football MVP** - at critical health, you consume no stamina
11.Hockey player** - two-handed heavy melee attacks use less stamina
12.Lumberjack** - increased melee headshot damage
13.Marine veteran - crouching enhances rifle precision and reduces recoil
14.Martial arts master - shoving deals damage
15.MMA fighter* - reduced damage from attacks
16.Nurse - heal yourself and others faster
17.Police sniper - damage falloff on heavy rifles is reduced
18.Prepper - increased ammo from pickups
19.Rescue specialist* - carry more medical items per stack
20.Sheriff - shotguns fire more pellets
21.Sous chef* - easier to dismember zombies
22.Spinal surgeon - one-handed melee attacks consume more stamina but do more damage
23.Swim captain - increased maximum health
24.Track star** - increased stamina
25.Quartermaster - larger ammo stacks
* - good Responder
** - very good Responder