For the no password I use puttygen.exe to create my ssh keys. I then specify it under connections, SSH, Auth and point private key for authentication to the private key you generated with puttygen.exe. (save as your default settings.) Copy the public key to your ~/.ssh/authorized_keys file.
on the shortcut I use to lauch putty I specify the path to putty.exe and then user@servername
as for passing the tail -f /whatever/log/file you could easily create a alias to do that (I'm not sure how to pass that via the putty shortcut).