CALLING ALL GAMERS! Question about Nintendo

I hope you can help me figure out what I need!

My kid has a Nintendo Gameboy Advance and I want to get him a Gamecube so he can play the games on TV.

I know I need an adapter but I see one adapter that is a little box deal that costs $50 and another adapter that is a cord that plugs into the Gameboy (or so it appears) that allows you to play the Gameboy games on the TV.

I really have tried to research this but I am not getting a clear answer.

Which one do I need?

Better yet, which one do I want?

If I want the more expensive one, why do I want that one?

I appreciate any help you can give me.

Thank you!