Both is actually what I do. First off, trackballs are the way to go. I go with Logitech mostly but have a Kingston and an Elecom. After 20 years in the market, trackballs are still not mainstream but only because people will not generally attempt to adapt to them. Use it for a few weeks. Once you get past the learning curve and develop muscle memory (like with most new hand coordination task) you will never go back.
Since they have never quite caught on, they don’t get the cool features that mice get, like super duper DPI speeds or all the buttons. I utilize a gaming mouse for that and sometime use one in either hand. When I’m this mode, I’m using it just for the additional programmable buttons and place tape over the underside mouse sensor so there is no movement from this mouse.