black covers well so you will be ok with it
primer is only really needed for bare metal as that's what its designed for, if your item already has good sound paint on it you can simply key it and paint straight over it so long as both paints are compatibleGrey primer is usually only used if you need to eliminate darker colours underneath, which white would have trouble doing in as few coats. Either way, putting black on top of whatever primer you use, (even red), is immaterial as it will totally cover any colour underneath.