Hibernate has nothing to do with Saving energy.
Hibernate means that the computer is totally Off.
However when Hibernate Mode is On, the computer saves a copy of the RAM status to a file on the Hard Drive.
Thus when you switch the computer On again you save few seconds of the Boot since the saved RAM status is loaded automatically from the saved file into memory.
Standby means reduce or switch Off some of the computers peripherals while the computer is basically On.
It does save energy, so if a computer has to stay On all the time it is a good idea to configure the Standby.
You already took the first step by configuring the Monitor.
Depending on how you use the computer you can add the Hard Drive and other component to the Sleep.
Please note that if the computer is Networked, or Hook live to the Internet do not put to sleep the Network related components.
Putting them to sleep results in losing the connection.