On for hard drives. Maybe off for SSDs
Fast startup allows your computer to get up and running faster after shutting down. This is done by logging off your user and then placing the computer in hibernation. This saves data from memory to the hard drive or solid state drive. All data is loaded back into memory on startup and the system is ready to go again.
Why I recommend ON for hard drive users? Hard drives are not the fastest and for a small bit of extra storage space to hold the hibernation file, you can get much faster system startups. If you use restart, your system will perform the full shut down and restart procedure.
With SSDs this are pretty fast to begin with and space is sometimes more of a concern. SSDs also have so many...