Most of these attacks are harmless unless you use the affected software (static sites for public things help). For SSH disable password authentication (public key authentication is more secure and more usable with ssh-agent), maybe use a nonstandard port if you want to have shorter logs.
Reading logs is useful: it's how I found that I made a mail configuration mistake which allowed backscatter spam. (I also found many delayed/lost mails due to bad anti-spam solutions like requiring reverse DNS.)
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