I personally like trackballs with a large central ball where I can use all my fingers. I am aware Ploopy offers one. This style however has fallen out of popularity, but I've been using them since the mid-90s.
Just using your thumb for all navigation seems like an RSI waiting to happen.
Also I don't know who in the last couple years decided it's a "Trackball Mouse" it's just a Trackball in the same way it's just a "Trackpad" and not a "Trackpad Mouse"