You don't even need to key in root as the user - putty has an option for auto-login username.
Google for "public key authentication ssh" and you'll get hundreds of hits back with HOWTO's - it's a long-winded process. Basically the easiest way is to use PuttyGen to generate a key, make sure you export it as both OpenSSH and Putty. Put the OpenSSH key into the .ssh folder of the user that you are using and then copy it into the authorized_keys file. Put the Putty key into Putty so that every time you choose the saved session it uses it. After you've checked it (lots) disable password-based login in sshd_config (PasswordAuthentication no) and enable public-key authentication (PubkeyAuthentication yes). You'll want to read a HOWTO because there are a lot of places to fall down if you're not looking (root logins enabled, etc. in your case).
I would suggest a passphrase on your key too but you seem to want everything automated - in that case make sure you key file is secure.
I have this set up (though not for root - be careful what you're doing). A certain saved putty session of mine connects to my server, auto-logs-in as my user using that key, the key has a passphrase, so that's needed as well, then once it's authenticated it sets up all my port-forwards etc. Basically a double-click and a passphrases sets the connection up securely and effortlessly. It also makes sure that options like Compression, SSHv2 Only etc. are enabled.
Last edited by ledow; 11-13-2007 at 05:41 AM.