Protocol version 1 has been deprecated, so I will answer the other half of this question only.
The root access via SSH can be dangerous, if anywhere else than on a local network, where it actually can be very useful for managing stuff without passwords.
Make sure first, that you had set up your public key, which how-to you can find all over the place or the internet for that matter, so I omit it.
Once you had exchanged your public key with the server you will be connecting to, be sure to just test if password-less SSH login works, and then you may edit with sudo or as superuser the /etc/ssh/sshd_config on the target machine to contain the following:
# allow my public key only, never a password
PubkeyAuthentication yes
PasswordAuthentication no
AuthenticationMethods publickey
PermitRootLogin prohibit-password
The above will make sure no passwords are to be tried and also root can be accessed via SSH directly.
Now to harden the security if you rented a VPS (virtual private server) someplace you do not have physical access, it is usually wise to disable root access, and use some ordinary sudoer, and changing SSH port or other less known techniques.
Recommended know-how sources to read: