
Mind you, its hard to learn the japanese terms. Red can be any of this: Hi, Aka, Beni. Ki is yellow, Orengi-Orange. Gin= gold Kin=Silver refers to the shiny aluminum foil scales, in combination ginkinrin means they have three rows or better of those scales from the dorsal fin extending down the sides. Combinations of those refer to scales/color/pattern.
So, sounds like Yamabuki's(gold/yellows in butterscotch or caramel shades) and maybe sanke or showa, depends on the markings.
red & white is generally a Kohaku, but depending on the blocks of red, it will either be 1,2,3,4 or 5 step. The breaks between the red should be clean. Black on Koi is generally referred to as sumi and you would mostly see that reference in say like my Bekko, you should be able to see it in depth, like its fadeing down into the fish, or "riseing" up, lacquer black. Reds should be strong as well.
The term Doitsu means no scales or few. My Shushui are actually a Doitsu version of Asagi.
Oh, its considered good luck to have at least one "ghost fish" A black koi in pond.
I like them about the one yr old age, old enough to be fairly hearty, but you get to watch them grow.

Also gives you a fair idea of what they be like in the coming years in color. And they do change, some will hold there colors and go deeper while some for unknown reasons will loose color or change completely. Most seem to stay true!