How VPN works?

Hello folks,

 

I am about to get NightHawk R7800 for VPN purposes. And i have no idea. I looked at online to get some clue. What i understand is even tho i have the Open VPN service i still need to get a membership from one those providers to use VPN locations?

 

My goal is to get a router that makes minor protection such as hiding my IP to create a tunnel for my privacy just using the modem itself. 

 

Do i have to pay for the service every month to do that? 

 

And as far as research goes encription is available on the R7800.

 

If VPN service is paid service and If i am going to use this modem just for one device do i really need to get the router since these providers allows you to use VPN service on the web?

 

What is the benefit of using VPN router for a single device if VPN providers are allowing the web browsing without the VPN modems?