Bare Minimum Required Items to play FFXI:
-PS2
-Controller
-Game
-Harddrive
-Network Adaptor
-Phone Line/Ethernet Cable depending on your internet connection (Cat5 ethernet is fine)

Extras
-Wireless connection: Wireless router + wireless adaptor. The wireless adaptor should come with an ethernet cable, because it will need to plug into an ethernet port (provided by the network adaptor).
-USB Keyboard. If ye don't have a keyboard to play this game, it could be a bigger pain than it usually is.

To play wirelessly, it will cost extra. If you don't have a wireless router already, you'll have to get one in addition to the wireless adaptor. If your modem is close enough to your PS2 and TV, you shouldn't really have to get one and could just use the 5ft cable you already have, or pick up a longer one.