Before I get into this - I'm in the US. YMMV if you're located elsewhere.
Also, I've only done this once, and I freely admit I likely have some of this wrong.
So an experienced author friend said to only publish the ebook to Amazon and don't use an ISBN since Kindle doesn't need one. Do one for EPUB and one for paperback and upload to Ingram Spark - Ingram will print ALL print books and sell to Amazon and others. It will pull from Ingram after awhile and show up on Amazon.
This is I think both a little vague, and dependent on what you want.
If you're Amazon-exclusive, you don't need an ISBN for either print or ebook - KDP will provide you with an ASIN. ASINs are meaningless outside of Amazon's distribution channels, though.
If you want the potential for your book to be available outside Amazon, you want to use KDP's Extended Distribution program. For that you'll need an ISBN. Interestingly, Amazon uses IngramSpark for distribution to other retailers.
However - and here's the big reason some people use IngramSpark instead of/in addition to KDP - Amazon doesn't allow you to set a wholesale discount at a level commensurate with other publishers. This means a place that might otherwise stock your book is unlikely to do so. (I don't know how it affects libraries; library pricing is kind of opaque to me.) IngramSpark allows you to set a wholesale discount up to 55%, which (from what I've read) is industry-standard.
That said, even with IS's discount, a bookstore is unlikely to organically stock your book. But if you're looking to distribute outside of the US and outside of Amazon itself, IS will allow you to do that as well, so if that's part of your plan it's worth it. You do give up some of the KDP-exclusive promotion opportunities if you do this, so it's worth thinking through.
Until recently, if you wanted a hardcover, you had to use IngramSpark. Someone here recently posted KDP has started doing hardcovers as well, so that changes the equation too.