I had been trying to afford a Unix installation at home as a CS student. All I knew was the Unix vendors. I was not aware of the social structure of the Unix world, various distributions, etc. I was crawling university surplus lots and calling Sun and DEC on the phone to try to find a complete package that I could afford (hardware + license and media). Nothing was affordable.
I was also a heavy BBS and UUCP user at the time over a dial-up line. One day, I found an upload from someone described as "free Unix." It was Linux.
I downloaded it, installed it on the 80386 hardware I was already using, and the rest is history. This was 1993.
So in my case at least, Linux became the OS of choice becuase it had traveled in ways that the other free Unices didn't. It was simply available somewhere where I was.
This isn't an explanation for why Linux ended up there instead of some other free *nix, of course, but by way of explaining the social diffusion of the actual files, I saw Linux distros as floppy disks around on BBSs and newsgroups for several years, with no hint of the others.
For someone with limited network access (by today's standards), this meant that Linux was the obvious choice.
As to why Linux was there and not the others—perhaps packaging and ease of installation had something to do with it? Without much effort, I recognized that the disks were floppy images and wrote out a floppy set. Booted from the first one, and followed my nose. There was no documentation required, and it Just Worked, at least as much as any bare-bones, home-grown CLI *nix clone could be said to Just Work.
I had supported hardware, as it turned out, but then Linux did tend to support the most common commodity hardware at the time.
My hunch is that Linux succeeded because it happened to have the right drivers (developed for what people had in their home PCs, rather than what a university lab might happen to have), and the right packaging (an end-user-oriented install that made it a simple, step-by-step, floppy-by-floppy process to get it up) while the other free *nix systems were less able to go from nothing to system without help and without additional hardware for most home and tiny lab users.
For comparison, I tried Minix around the same time (I can't remember if it was before or after) and struggled mightily just to get it installed, before questions of its capabilities were even at issue. I remember my first Linux install having taken an hour or two, and I was able to get X up and running the same day. It took me much longer to get the disks downloaded and written. Minix, by comparison, took about a week of evenings, and at the end, I was disappointed with the result.