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Lol as your intro implies, this is a pretty redundant question. Just look around and it has been discussed many times on the forum... But I'll answer anyway.
A model must be put on the appropriately sized base that it comes with per the rules. The Prince comes with a 40mm base, so the rules state that you should put the model on said base.
However, the rules also state that if it is okay with your opponent, you may use a larger base if desired.
So, if you want to ask permission every time you play, than yes, go with a 60mm base. If not, take the 40mm. And as far as the Greater Daemon goes, I'm pretty sure he goes on a 60mm base.