A few quick items:
1) I agree with all who posted. You should have no problem leaving the Mini on indefinitely.
2) Go to your System Preferences and select the Energy Saving Option (It looks like a light bulb). Check off to turn the Hard Drive off when possible, Select Sleep, Never and set your monitor to power down when you want it to.
3) If you have a broadband internet connection where it is always on, you want to make sure your firewall is up. Go to System Preferences, select Sharing and then select Firewall. Turn it on for your protection. You probably don't need it if you have a router, but just in case.
Good luck!