Own 'em all. For a given definition of "all".
I used to be a "big knife better" advocate, until I tried using one for everything. I began to believe that a knife should be part of a larger set of tools.
Sure, they're not like sockets or drill bits where you need one in every size graduation plus letter sizes and reaming tools (although if that's how you collect, I'm not here to stop you). There is some overlap, and I've found that a 3" blade takes care of most things, as long as it's the right shape. There's a wire stripping blade on my Alox that gets used for smaller work, and it would probably handle all the precision tasks that aren't enough for the 3".
Going up from there, I find a nice compromise around 4" for rougher work, and I think I would switch to a saw or hatchet, after that. But I'm a town boy, not a bushie, so I might be talking out the wrong hole. I know there are people who go right to a 9" blade or a machete, and they do everything they need with it.
You mentioned "must haves" for a deserted island.....
Well, I'm obligated to say "Smatchet", and it actually isn't a bad choice. But from the context of your post, I'm allowed four.
Hmm.
A Kukri. Something on the larger side, but I would have to experiment to see exactly what. About a 10" blade seems right, acceptable chopping power without being impossibly large. I'm looking to harvest firewood, not build a log cabin.
A machete. Ontario, Tramontina, Imacasa, take your pick. Good for lighter stuff.
Down to that all-purpose knife I talked about earlier. Becker BK-2 comes to mind, although it's a little larger than what I strictly want. It's also inexpensive, almost indestructible, and I can touch up the edge on a rock.
Last one would be something like the "Otzi knife". Who am I to argue with history?
Hey, welcome to Bladeforums, by the way. I like your enthusiasm, just remember that most people around here have a goodly amount of snark, but aren't really out to hurt anyone.