In order for me to go online with PS3. Do I need a router to connect to my PS3 adn computer? Or just a router?

Answer 1

A router will be fine. If you have a computer, it can share the router with the PS3. If you only have a PS3 (that'd be weird), you might not need a router; you just plug the Ethernet cable from the cable modem to the back of the PS3.