What you get is completely unpredictable--white turns OFF the display of genetically present colour and pattern genes, so they can't be selected for or against. All you can select for is type and traits that don't relate to plumage colouring.
If you breed buffs, you will select against birds with a smutty undercolour and for birds with even colouring. If you breed blues or blacks, you will select against birds with colour in their hackles and for the blackest of black or for blue that is not so dark that you have to guess whether it is blue or black. If you breed partridge, you will select for vibrant colouring, good penciling in the females and black breast in the males. Etc. Birds with poor patterns or poor colouring are removed from the breeding pen.
Consider if you will, breeding a buff to a partridge, then taking those offspring and breeding to a blue, then back to buff, then to black, then to red, then to grey, then to parrtidge then to .... What colour will those birds be? And what genes will they pass?
This is pretty much what that white is underneath the white OFF switch--generations of mixed colour breeding. With the exception of a double dose of white, every white bird is genetically unique from every other white.