I was first introduced to the mouse when I studied Manufacturing Engineering at university, and spent as much time in the computing labs as on my course. That was a world of Sun-3s and Sun-4s, running SunOS, a commercial version of Unix. Before then I'd seen mice, but never used one. All my home computing had been entirely keyboard based, and at school we'd used CP/M for what little computering was taught.
I found the mouse to be a wonderful device, intuitively easy to use. All you had to remember was which of the three buttons did what and when to single- or double-click. However, even then I was aware of its limitations. I had previously used a light pen as a pointing device. Light pens famously suffer from the "gorilla arm" problem, and it was immediately obvious that the mouse has the same inherent design flaw, although to a lesser degree.
With a mouse you don't have to support the weight of your arm, the biggest problem of a light pen or a fixed touch screen, but you do still move your whole arm around, even when making very fine movements with the mouse. This strains the muscles of the upper arm and shoulder as you use them in ways that they are really not optimised for. This is bad ergonomics. It can cause injury, and also makes fine control difficult.
But mice were what we had, and when I bought my first vaguely modern computer - a PC running Windows 3 - that too came with a mouse, and I learned to use it like a champ.
Then during one of the industrial placements that were part of my course I saw a draughtsman using a very different system. His workstation had three different input devices. There was a keyboard which he didn't use much. There was a pen-based input system that lay flat on the desk in front of the keyboard, which he used to select the various tools in the CAD system. That was rather "gorilla-ey", like a light pen, as the systems of the time couldn't discriminate well between him pressing the pen onto the surface and his hand lying on the surface. But then there was the third device. It was another flat panel, which had a ball embedded in it with buttons around it - a trackball. He used the ball (which he rotated with his thumb) and combinations of buttons to drag points around, place them, rotate the whole view in three dimensions, and so on. He used it how I used a mouse at the time, and it was obviously a vast improvement. While using it his arm didn't move, he didn't have to keep picking the mouse up to move it back from the edge of the desk, and he could easily make the most astonishingly fine movements with it, using the muscles that are "designed" for fine manipulation.
I wanted a trackball myself. It was almost three years before I found one that would work with a personal computer, and I've used one ever since, for nigh on 25 years of professional computer-wrangling. I've never had any of the joint pain that so many full-time computer users complain of. I don't need a big empty space on my desk. And best of all, I'm doing my bit for the human race as cats don't chase trackballs and so won't use it to take over the world.
So, now that I've convinced you that you should use a trackball - which one?
For a very long time I was an advocate of the Logitech Trackman Wheel. Only available for right-handers (sorry lefties) but Logitech discontinued it nearly a decade ago. Their M570 model is basically the same ergonomically but has one terrible flaw: it is wireless. This means that you have to change the battery ever so often, and you just know that it will go flat at the most awkward time possible, because computers are sentient and hate us. Even more unforgivably, it doesn't even use Bluetooth, it uses some proprietary wireless protocol and its own USB dongle. For those stuck in the mouse dark ages wireless devices make sense, as you don't want a trailing cable moving around and catching on things, but with a stationary trackball that's not a problem, so a wired connection is obviously superior.
The Trackman Wheel is still available from places like Ebay, but can be quite spendy. When mine finally gave up the ghost recently I had a spare available but of course I needed to find a replacement so I could restock the spares box. Ebay was in a being-overpriced mood, so I looked around for ergonomically similar alternatives that also met my requirement of being wired. I found the Perixx Perimice-520. It is just as comfortable as my trusty old Logitech, and has a rather nifty feature I've not seen before, you can push the scroll wheel sideways as well as up and down. Again, it's only currently available in a right-handed configuration, but the company do at least have some left-handed products, so there's hope that a left-handed version might appear at some point.