It's cheaper to shut it down and then turn it off at the mains than to do either of your options. Both of those still use some power.
Next best option is to turn it off using the "shutdown" option.
This still powers some of the mainboard etc. in case you have "wake on lan" or "wake on ring", or a keyboard which incorporates a power button, or various other functions. Not a lot of power, but it's considerably more than just a red LED.
Then Standby. This mode means that your computer has to keep more onboard functions going; depending on your BIOS settings it might do a "suspend to ram" type function, which means the mainboard still has to power the memory and memory controller.
It's also not true to say that turning things off will extend the life of your computer.
Turning power supplies on and off sends big power surges through the power supply - both for the computer and (if separate) the monitor.
Often, electrical devices will function for longer if left turned on.