You can make a .tar.gz of the web site like this:
tar -pczf backup.tar.gz /path/to/web/site
This will keep all permissions and ownerships. You can then transfer the .tar.gz to the new server with scp...
scp backup.tar.gz root@srv2:/path/to/directory
(replace srv2 with the full hostname or IP of server2)
... and there you can uncompress it like this:
tar xvfz backup.tar.gz