Based on the edges of the shirt, it's obvious you have motion blur. Based on some other subtle clues (e.g not every high-contrast edge is blurry), it seems that it is the motion of the subject rather than the camera.
You may also have some focus blur, but the main blurring seems to be motion.
That slow of a shutter speed is pretty much guaranteed to have sketchy results. I would shoot no slower than about 1/500 sec. Boost the ISO if necessary.
You also have some fairly bad chromatic aberration going on. I love large apertures, but in this case you might consider a smaller aperture. In this context, at some point it will come down to a balancing act of evils between chromatic aberration, high-ISO noise, and motion blur.
In circumstances like this, I sometimes purposefully shoot several shots with a slow shutter speed, about 1/60s. The idea is that I might get a tiny % of those shots that are beautiful in terms of low noise, and might even have some artistic-looking motion blur. (Especially if the camera is tracking the subject and it is the background that has induced motion blur.) I also try shooting with fast shutter speed, reasonable aperture (e.g. f/8.0), and high ISO - so that I know I'll get some good "fallback" shots with the exception of ISO noise. (Otherwise, I prefer wide-open aperture for shallow depth-of-field.)
Personally, I usually lock the shutter speed and aperture, and let the auto-ISO do the adjustment. I also shoot with a full f-stop of underexposure bias, 1) for additional flexibility, and 2) you can pull detail out of shadows but you can't recover blown-out highlights. (With a full-frame sensor, I can afford to pull low-noise detail out of shadow, unless I am going for absolutely 100% color and detail fidelity under tightly controlled conditions.)
So, if you are almost always going to do post-processing, then yes do shoot in raw format, and try my trick of purposefully underexposing your shots. But a raw workflow is substantially slower - and gets exponentially slower with a linear regression backward in computer hardware time and cost. (I use raw but for cameras that can't shoot in raw, my workflow is so much faster.)