I recommend the thumb controlled versions. I use the Logitech for everything I do on the computer. I've also used it connected to a laptop and had it sitting on the chair arm or resting on my leg. I use a cordless version to control another PC hooked up to the TV but I prefer the wired because I got tired of batteries going dead at inconvenient times.

The advantage of the thumb controlled version is that your left and right click fingers never have to leave the buttons. The advantages for gaming are obvious but for general computing it's just more relaxing in my opinion. The Microsoft Trackball Optical pictured above is discontinued, I think, but those extra buttons are a nice feature. The extra programmable buttons on the Kensington tempted me enough to buy one but the large ball requires a lot more hand movement to operate.
I've been using a trackball for so many years I've forgotten what the learning curve is like. Whenever I set up a new computer I have to adjust the cursor movement speed higher than the default. Finding the sweet spot can be frustrating if you have a twitchy thumb.