For graphics design and such, a trackball where the ball is located in middle are probably best. But there aren't many options for general purpose (including gaming) trackball, these trackballs have their balls located within reach of your thumb.
Logitech M570 is your best bet for thumb-operated trackball right now. This however means that you will lose a thumb button. M570 does have two small buttons next to first mouse button, but whether you can conveniently use those or not depends on reach of your index finger. I've never bothered myself because locations of those two small buttons weren't comfortable to me, so I've been using M570 like it has only two buttons if you don't count scroll wheel button.
Been using M570 for about 10 months now at work and at home. I couldn't go back to normal mice. I play all my games using M570 as well, including shooters.
Word of warning though. You WILL need a lot of practice to learn to use M570. I required several days of practice before I got used to it in normal desktop use. Two weeks of practice to get used to gaming with it. So don't expect you can just switch over to a trackball and play games as if nothing's different, you will have to adjust. But really, it's worth it.
If you do get a thumb-operated trackball like M570, don't try to roll the ball using tip of your thumb. You should soon notice that your thumb movements are shaky and inaccurate. Try to control the ball using the area between tip of your thumb and the first joint. While learning to use the trackball, you may want to lower cursor speed as well. As you get more and more used to a trackball, increase cursor speed until you reach your comfort zone.
Additional tip. I've never liked Logitech software's cursor acceleration, I much prefer Windows' built-in acceleration feature which is called enhance pointer precision. A lot of gamers hate this because it makes them inaccurate in games, or so they say. But it's all about adjusting and learning, you can be just as accurate with it as without. But I couldn't live without it whether I use a normal mice or a trackball. You should try cursor acceleration on and off and see which you prefer, while learning a trackball is as good time as any.