"Mandrake 10 or Fedora Core 1? Which is more stable?"
I don't think that you will have stability problems with either distribution.
"which would you use?"
I strongly prefer Fedora to Mandrake for reasons that have nothing to do with stability. Since this is your first install you should go to the public library and check out a book on the latest version of Red Hat that you can find. It will be a reasonably accurate guide to installing Fedora.
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Be prepared. Create a LifeBoat CD.
http://users.rcn.com/srstites/LifeBo...home.page.html
Steve Stites