Hi Tangram. I think it doesn't matter if you buy 9mm ammo or a .22. You will learn things either way. If you want to get better with the Kimber, I'd buy more whitebox. You'll learn to get better with a particular gun by spending time with it (at home dryfiring it, and at the range). A different gun will index different, will have another trigger to get used to etc.
If you want to become a really good shooter with the Kimber, I'd even lean towards not buying white box or a .22 and investing the money in a nice reloading press.