Evoluent Vertical Mouse. They should really start paying me for constantly plugging them. The first time I tried one it was pretty much, "Yep. That's my mouse." This is an experience shared by a non-zero number of people who've tried my mouse. YMMV.

Wrist things?

I've tried out about a dozen different kinds of mouses (including the Vertical Mouse), and my favorite by far is the AirO2bic quill mouse. My second favorite was the Whale Mouse which appears to have been succeeded by the Switch Mouse.

I envision a wrist thing as one of those little gel pads that I would rest my wrist on to use with my current mouse.

Also, I have a somewhat small hand for an adult. Maybe I should go to Best Buy or Costco and try a bunch out before I put in a request at work...

I don't have small hands, but I prefer small, lightweight mice. The overall best mouse of this type currently available is the Microsoft Compact Optical Mouse 500. I bought one last year in white/grey for a friend who always coveted my long-discontinued Kensington PocketMouse (early-2000s, not the later model). We really like the Microsoft mouse.

Beware, though – Microsoft had a crappy older model with the exact same name (including the "500"). The old version has separate pieces of plastic for each button and is of lower build quality as well as design.

How do you feel about trackballs?