-Seaman
Seaman enhance other sailor's ability. His stat determines amount of stat revision, thus it's important to have seaman with decent base of stat of your desire.
-Restorer/Engineer/Repairer
Restorer basically increase your ship's Soft Defense (SD), which convert direct damage into burning damage. Instead of taking damage immediately, having higher SD allows ship to sustain damage over time, allowing ship to repair. However, SD is capped at 900, which is often easily obtainable for most of BBs. All sailor's restore stat count toward ship's SD.
Engineer increases ship's OverHeat(OH) speed as well as duration of OverHeat. All ships has speed cap and engineer does not increase speed after that point. However, OH duration doesn't have cap, so Engineer is most important sailor among BB crew. Engine stat only works on this class of sailors.
Repairer is sailor with high repair growth stat. Because all sailor's repair stat count toward ship's repair speed, player often have fewer number of Repairer than Engineer.
-Medic
Medic reduce chance of crew death during battle that can be caused by getting hit. However, it's not used much nowadays because Medic doesn't work on BB and CV no longer lose Veteran (Officer) for pilots.
-Sonar
Having Sonarman on board allows player to detect nearby merged Submarines, But CA and BB cannot detect Sonarman even with Sonar on board. SS's sight is harshly limited without sonarman.
IJN Torp sailors.... I never played IJN so I do not have info on those.
Hopefully this helps.