While the original question was about Google Sites, these rules apply to any webhost.
REQUIREMENTS FOR HOSTING YOUR WEBSITE
1. Have your own domain name, preferably your name or initials. You want your stuff branded with YOUR name/company/imprint, not anyone else’s. For example, this blog is hosted on blogger, so you can actually reach it via ideatrash.blogspot.com. But most people know it as ideatrash.net (and when/if ideatrash.com comes up for sale at a price I can afford, that’s gonna be mine too).
2. Be able to move your content by simply downloading and uploading (and keep a copy on your local computer). Let’s say the webhost screws you over. Or you outgrow the service they offer. You don’t want
to spend the time recreating your whole website from one “template” to another – you want to be able to
download your files, upload them elsewhere, and then just point the
domain name at the new host.
As long as your solution can do that, it’s up to personal taste. Personally, I use Namecheap for both domain names and webhosting.