I'd be curious how many games you've played before and what your comfort level is with difficulty. I'm going to mention the ones on that Collector's Disc first. "The Legend of Zelda" is the first game ever released. It's also the most nonlinear and it has hardly any direction in it about where to go. It's a good choice if you really want a challenge. I'd recommend finding a non-spoilery map, though, unless you plan to draw one yourself. It can come in handy.
"Zelda II: The Adventure of Link" is one I can't speak for personally, as I still need to play it. But I know that it's the only side-scrolling game and it's also a good one if you're really looking for a challenge.
"Ocarina of Time" (commonly abbreviated OoT) is iconic and the first one I've mentioned that's 3D. If you're a frequent gamer you won't have any trouble with it, but it still has a fair amount of difficulty and it has more story than the ones that came before it. It's actually pretty balanced compared to the previous titles and some of the later ones.
"Majora's Mask" is a direct sequel to OoT. Again, if you game frequently you won't have trouble with it. If not, I'd recommend starting with OoT and then playing MM to get the hang of the puzzles. There are also a lot of sidequests in this one that are easy to miss if you're not inclined to look for them.
Moving on to those games released for the Gamecube that aren't on the Collector's disc. One is "The Wind Waker." It contains references to OoT, though you can still understand the story without playing that. Enemy difficulty is easier on this game compared to earlier games, but it's still easy to miss the sidequests, and sailing can get boring if you're the type who wants to go from plot point to plot point without exploring. I personally don't mind it (sailing) as long as I'm exploring islands and using my treasure maps, though.
And the last I'll mention is "Twilight Princess." Also has easier enemies, and it's pretty good about telling you where to go next, and in that respect it's a good intro to the series if you've not played many games in general, not just Zelda. Plenty of fans who have played multiple games, self included, have it as a favorite, but others felt it was one of the weaker ones. Obviously no way to tell for yourself until you've played it, but again, I mention it in case difficulty is a factor in your decision.