what are the units for density and when do you use each

Every unit of density is
(a unit of mass) divided by (a unit of volume) .
The one most widely used is [ gram/cubic centimeter ] , but there's no reason that you MUST use this same unit every time you talk about density. You can use (any unit of mass) divided by (any unit of volume) that you want ... the best choices are always the ones that end up with the most convenient number.
Whatever units of mass and volume you decide to use, it's easy for anybody to convert it to [ gram/cubic centimeter ] if they want to.