Re: Lives Questions
If you hunt around, you could probably find a Gamecube at a used game store for less than $60 (American dollars) easily. The least I've ever seen an XBox (original) listed for was $119.00. Thus, there's a major difference between buying one of the two listed consoles if you're not looking to spend any extra money beyond the $80.00.
With that in mind, you could probably get a used Gamecube and one game to start with for about $80.00.
The true question is what sort of games are you interested in?
If you're into sports, racing and shooter games, to mention just a few genres, then an XBox would most likely be the way to go.
If you're a hardcore fan of the franchises Nintendo created (e.g., Mario Brothers, Metroid, etc.) and (for the most part) more family-friendly games, a Gamecube would be the direction which I would direct you towards.
Then again, you could do like projectego suggested, and start saving up for a XBox 360 (or Wii).
Hope that helps....
Edit: It seems I might have been confused...do you already have an XBox, and are wondering if you should get some games with the $80 to go along with it? If so, take the information I gave you regarding XBox games in mind.