Typically standard NM-B cable is used (often called "Romex", although Romex is actually a brand and they make other kinds of wire as well). You'd use 14/2 + G (two 14 gauge conductors with an additional safety ground) for 15A circuits, and 12/2 + G for 20A circuits, of course with appropriately sized breakers in the power center.
Note that NM-B cable is not for use where it's exposed to the weather, or where it would be flexed in use (such as leading to a slide-out). 120V runs underneath the floor, if any, should be of a wire type that's rated for wet locations and properly protected from physical damage in conduit or something similar. Usually in RVs 120V wire is not generally run under the floor at all. Other types of wiring could also be acceptable, if less common, as laid out in the National Electric Code.
The 120V section of the power center is wired like a subpanel in a house, with the neutral and ground kept separate, and the ground should be bonded to the chassis of the van.