You can install Linux on a 1.44MB floppy disk, so yes. It won't do much, but can be useful for troubleshooting.
Linspire is a good newbie-friendly distro, but since it is so radically different from many other distributions, I would recommend staying away from if you really want to aim for a more "normal" Linux experience. A lot of people are having success with Ubuntu, which generally sets itself up pretty well. Alternatively, Fedora and OpenSuse are good choices.