Do you need a connection to the Internet/WIFI to use the PlayStation 3?

Your straight out of the box ps3 does not need an internet connection. But games, even on disk, might need system upgrades or game patches to fully work, even for the offline modes. Once that is done, you'll be able to access offline game modes without any connection. You won't be able to access any online features of course.

You can turn on/off the Wi-Fi connection at any time in the xmb menu.

Your ps3 also allows full parental control if that is a concern to you. Always remember that online interactions with other players could exceed ESRB ratings.

Finally, your ps3 has plenty more to offer with an internet connection. It's an effective platform  to fully enjoy your  Netflix, CrunchyRoll,crackle, NFL network or Spotify account and get more from that older 'unintelligent' TV.

I highly suggest connecting to internet with the Ethernet wire. Online gaming and streaming will be more stable than with WiFi.