I have found (actually, I simply "bumped upon") some links to A SUBSTITUTE to an AT&T- (wired) home telephone setup.
What sort of setup is a V.O.I.P. (Voice-Over Internet Protocol) system? If I do use this system instead of my wired telephone setup, what hardware will I have to use?
%Will I need to leave my P.C. powered up and running all day and night long to continue an access to this system? Am I correct to assume if I turn off my P.C, I will not be able to make or receive calls?
Thanks for feedback.

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VOIP is an interesting service. You must have power and you must have a working internet connection with high bandwidth.
There are many programs and vendors. Some of them require a headset bluetooth-connected or USB connected to your computer. Others use a router with a telephone jack in addition to the usual ethernet jacks and almost any sort of plain old telephone will do, even the base for a cordless phone.
Skype is one that works through your computer. Vonage is one that works like a regular telephone except that 911 calls work a little differently. Some cable providers offer phone right along with internet and cable TV, for example, comcast.
Skype and Vonage are the easiest services to take with you when you move from place to place. For example, If you move across the country, you take your Vonage router with you and hook it up to your new internet connection, and it will work (good idea to change your local number to the local area code, but if you buy the 888 service, that number will work right away).
Skype requires your PC powered up. Vonage requires only the router and internet connection active.
The service I have also emails me the .wav files from the messages people leave, and there is even an option for those messages to be translated to text and emailed.
Even Microsoft offers some sort of VOIP. (Shudders to think of the horror show that probably is)