The builder is the first role you'll want to assign to a character, as these are the characters that perform all construction tasks, such as building new rooms or furniture.
WARNING: Current issue? (Alpha 1b) Builders sometimes have an annoying habit of staying outside until they have only 1-minute of air, then they will return to an airlock to replenish their suit's oxygen supply. THIS IS NOT long enough! Usually the builders will die inside the airlock just as it closes. Make sure you build in stages and do not assign one large task in order to avoid this.