Keep Mac ON for background work with minimum power
While newer Mac OSX offers something called PowerNap, the feature does not support the uses you listed. Therefore, the only options are within System Preferences. 

In this case, you should set your Energy Saver settings to Computer Sleep- Never, and Display sleep - 1 min. Check the box for 'put hard disks to sleep when possible'. Wake for network isn't helpful, since your computer will not sleep.