Please note that I write Google first and then Microsoft is for the sake of alphabetic sorting order only not for preference.
My preferences for buying a domain is from godaddy, as they provide simple dns management.
What is your preference?
Google offers Google Apps for free and Microsoft also offers freebies like Windows Live Admin Center and Office 365 in the form of [email protected].
So what are the differences? Let's see, I will not go into details:
Account/Users: Apps: 10; Live: 500; Edu: unlimited (at the moment)
Administration: Apps: Admin; Live: Self-Service; Edu: Admin
Mail system: Apps: web-based; Live: hotmail; Edu: Microsoft Exchange 2010
Mailbox creation: Apps: Admin; Live: Admin/Self-Service; Edu: Admin/Self-Service
Storage: Apps: 7 GB; Live: 25+ GB (include skydrive); Edu: 25+ GB (including skydrive)
For me Google has more advantages in maturity in Cloud Computing, but Microsoft has support from rich client support (read Microsoft Office) and Microsoft is more generous on storage.
So which one will be your preference?