Its more like, the characters you play died in the normal/real world and were offered reincarnation into this new world while still keeping all of they're memories and appearance intact. 

As far as classes go, be creative. Just use the 3 categories as a base; Warrior, Mage and Thief. If your a 'swordsman' that falls into a warrior class so your stats would reflect higher physical stats then a mage. Stats will only matter when it comes to learning new attacks which there will be 1000s.