If you go for a trackball, get one with a fairly big ball, like a Kensington Expert Mouse or CST LaserTRAC. Tiny balls
(don't let it wear a kilt, or other people will know!
), like the Logitech Trackman Marble or Kensington Orbit, can help cause strain, lacking momentum and being tricky to get precision position with, without trying to hold your wrist and knuckles in place. The higher-sitting ball also makes it easier to find room to position wrist rests, should you need them, compared to short ones, and the big ball let's you just roll it in a direction to go across the screen.
Logitech's Optical Trackman aught to be OK, but they don't make a corded version, which, IMO, sucks, because I'd buy one if they did. Screw batteries. I used to have its competition, MS' Trackball Explorer, to which there is no USB-power competition, today, and it was awesome. Sadly, it was awesome enough that there is a healthy repair market, and on both of mine, it is the plastic loosening over time, not the switches, that were a problem.
Then, with a trackball...
I guess it depends on what you do, but I have tried, and precision drawing or graphics work with a trackball is truly an adventure
Make sure, in Windows, to apply Mark C's mouse fix at your preferred DPI. Vista and 7, and probably 8, do have some idiocy left over from Vista wrt to the mouse. Turning the sensitivity down a bit, with no acceleration, work fine for graphics work. Acceleration makes it practically impossible, though.
Thumb strain? Your thumb is the most versatile finger you have with way more mobility than all your other fingers combined. No such thing as thumb strain.
Maybe if you practiced moving your thumb around in intricate shapes as a kid, or maybe got lucky with thumb dexterity genes. Thumb trackballs hurt within a minute or two for me. Both my parents have the same problem. There is such thing as thumb straight, and those trackballs can cause it quickly.
I would definitely
not get a trackpad, but a larger surface, like a digitizer, might be alright.
I have no experience w/ the funky vertical mouse.
You could also consider a small joystick, using Xpadder or Joy2Key, as a more esoteric option.