It's exciting to find the first babies!
I vote goldies/shubunkin. Reddad35 is correct -- you need 2 to tango.
There are some reports of koi-comet cross, but they are rare and are probably accidental (meaning a pair of goldies were spawning at the same time as a pair of koi and something wafted into the area of the other.) The shubunkin and goldies are the same species and can breed together.
Koi don't usually breed until they are more than a foot long. Goldies do the deed very young and very often (could be every two weeks necessitating ruthless culling).
An early way to tell koi fry from goldie fry: Goldies stay olive/bronze until they are about 1.5-2" and sometimes forever. (I left a couple 3" juvenile sarassa comets in the lily pond last winter, convinced their olive/bronze color was the final color, only to discover they had turned red by spring.) Koi have color as soon as you can see them.
And as stated, koi have barbels (whiskers).