|You don't have to actually shut the computer down to recycle the power on the modem and router. It won't hurt anything, but it isn't absolutely necessary either.|
Some ISP's provide clients with a "combo device". That being a device that is a combination modem, router and access point all in one. So you'll either have one, or two devices on which to recycle the power. Obviously if you have one, there's no sequence to powering them down/up.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.