What Internet thingy should i get!

[WiiStar]

I have hi-Speed Roadrunner its like a black box And i was wondering What cord for wii internet or what ever should i buy

And Does it charge me any cash? to hook it up like does it charge a fee?

Please help i really want online soo i can Battle some of you!

If my post was Confusing! Message me ill tell you more but for now im just dont know the name of you stuff you need to get to play wii online!