Well, as far as logins go, you only want to see your IP, along with perhaps your provider or server management company, if any. You'll likely see a bunch of attempts, they'll say, "ROOT LOGIN REFUSED FROM xxx.xxx.xxx.xxx" or something along those lines. People are gonna try to login to your machine, nothing you can do about it. And if they do login as root, they can change the log files. So you might want to install tripwire and chkrootkit.
Ideally, you'd log in to SSH via a normal account and then su/sudo to root when you need to. It's not necessary, but it's a good idea to disable remote root logins.
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