I think that you definitely don't want your system going into standby or hibernate if you're rendering, anymore than you want a cat anywhere near the keyboard. Results probably vary for screensavers depending on the application, the system and the screensaver itself, but I'd disable them as well. I have my monitor set to  power down after 10 minutes of inactivity and that seem to work fine.

"Democracy is a pathetic belief in the collective wisdom of individual ignorance." - H. L. Mencken