Upgrade to new server

We are currently running SD 8211 on a Windows 2003\SQL2005 box and are looking to upgrade the entire environment to 9033 on Windows Server 2012\SQL 2008. We are also looking at changing the domain that the server sits on.

I was thinking that the best approach is:
Build the new server on the new domain
Load SD 9033 and create the database on the new SQL 2008 server (it is a seperate server)
Test the new instance, then step through the migration on the old server.
Once the old server is up to date, perform a backup, and restore the information onto the new 9033 environment.
Finally, I would need to rename the new server to what the old server is named.

Is this the recommended approach, or is it installing 8211 on the new server, then performing the upgrades there?

Also, for Single Sign on to work, it needs to reside in the same domain as the usernames and computers, correct?

Thanks,
Dave