When my PC goes into Standby I have to use the power button to power up again. I should only have to move the mouse or touch the keyboard.

Not all keyboards and mice support the ability to wake a system simply with a key press. To check if your device supports this type of action open the Device Manager, select the device listed in the Device Manager, and select properties. If the device supports Power Management a tab titled Power Management will be shown with options to allow the device to bring the computer out of standby. If these options are not shown, or not selected the computer may not wake when the system boots.

Some systems also disable peripheral devices when the computer is in a reduced power state, these systems commonly configure this option in the BIOS. If a given system has issues with not waking from keyboard or mouse input try adjusting the power management settings in the BIOS so that the system enters a lower sleep state (S2 as opposed to S3)