Domain name doesn't matter, unless you're signing with a public CA. I'd think self-signed vs internal CA vs public CA would depend on what the authentication mechanism supports and how you have to manage the certificates. (i.e. if there are going to be a ton of them it might be easier for the authentication mechanism just to trust certificates signed by a certain internal CA rather than having to make each certificate trusted.
From what I've seen so far, I've come to the same conclusion.