I had an old Logitech TrackMan, the kind where the trackball sits under your thumb and the buttons are under your fingers. Your hand rests comfortably across the base, it's pretty great for basic computer usage, but I ditched it when I got into FPSes years ago. Thinking about it now, I don't think I'd mind to grab another one.
However, if even resting your hand on your mouse creates trouble, I don't know if that'd even help at all. A low-end tablet might be worth a try, if holding a pen isn't a problem. I think the Graphire line is pretty cheap, and hey, if you like to draw in your spare time, I have a 9x12 Intuos 2 I'm looking to unload!
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