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if you'd like to get a taste of linux before actually installing it on your hard drive, try knoppix. it's a linux system that runs from your cd rom drive. just put it in your cd drive, reboot your computer, and it goes to linux. when you're threw, just take the disk out and reboot, and you're back to your original system. all the fun of linux without the commitment.
http://www.knopper.net/knoppix/index-en.html
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would have to be either mandrake or redhat as far as i'm concerned, they both have their good and bad points
redhat can be a bit ugly at times if youre new to linux (but you get that if youre new to something right?), redhat is probly the most widely used and you can also get it in boxed form with manuals and stuff too i think.
if you had the chance and ran into an old and cheap (not sure if its possible) SGI system, their version of linux / unix (they call it IRIX) get the thumbs up from me as many of the command line features also have a corresponding GUI solution, I have found this to be the best version of unix i have used apart from redhat 7.1
but for a regular pc i would go with redhat, thats just based on what ive seen though
as the_jinx says, get an external modem, theyre better and they will work with about any o/s you can throw at them