Shutdowns for anything longer than 30 minutes, using the 'hibernate' method gives several benefits: It's a near zero power state; all 'Startup' folder items are already loaded, Windows background services are already 'up', and all open work moves to the hard drive, yielding really fast start-ups.
And if power is lost (storms, etc.) the document or picture you were working on won't be lost like it would be in 'Standby' mode, and the system will resume just where you left it.
That's because things in RAM are moved to the hard drive.
"Sleep" is keeping things in RAM, but only some aspects are not working, like the display.
If there's power interruption, that RAM data is lost.
Laptops in Hibernate can be completely de-energized> moved> left sitting for months and when re-energized, will resume just where you left it.
I always use Hibernate, except when directed to 'Shut Down' or 'Restart' from an installation or Update.
On the Internet connection: yes it does take a few seconds to resolve your IP...just the way it is.
Firefox can be configured to resume just as you leave it:
To have tabs re-open when you start FF again:
Tools> Options> Main> Startup heading: in top slot, the drop menu, select 'Show my windows and tabs from last session'> OK out.
Then when it comes back, on the bottom of the main window will be 2 buttons: select "Restore session". It then goes back to the URL's you had at the time of shutdown, and reloads that page from the server.
I guarantee this is faster than reloading Windows.