I have slight hand shake due to an injury. I currently own a Canon Rebel SL1 (not stabilized) with a 24 MM F2.8 stabilized lens.which offers up to 4 stops of image stabilization (IS). Even with that, I found ways to minimize/eliminate shake , because I found, I tend to move more than I realize - I need to be very aware of my body and what I am doing when I shoot. I am a landscape / travel photographer and find things to lean against (trees, poles, etc), put my camera on (rocks, branches, sign posts, walls...), and also - as others suggest - found ways to hold the camera to minimize shake. It can take some experimentation to see what works best in holding a camera. And it works! For me too, setting the shutter over 125 also hopes. I found anything under that with my Canon might result in blurry images.
Keep in mind too, that aperture under about F/8 or so may look like it is blurred in areas but can be just depth of field.
I am upgrading my camera set up and image stabilization is important. I liked Olympus cameras or Panasonic/Lumix which offer stabilized cameras which folks can rave about. I was really impressed with the OMD M-5 from Olympus for the stabilization.
That said, I demo'd the XT30 and XT3 and found it very stabilized through lens stabilization. What sells the camera for me is the incredible amount of detail throughout the image that II can get and the stabilization. Of course I shot a photo of someone while moving and it blurred, but that was to be expected since i was moving.
Check photo below. I only decreased the size of it. This was just a quick demo with the 18-55 F2.8-4 lens. That detail, even in darker areas, sells me with this camera.
Last I would say go to a camera store and demo.
Keep in mind though when demo'ing that the settings the camera is at may not be what you need not bring out the full capabilities of the camera (happened to me quite a bit when demoing). As you learn a camera and its functions/capabilities, you will get better.
I suggest you mention the type of photography you want to do, mention the hand shake issue, and ask the salesman/saleswoman to set the camera for your needs. You might want to review the images with them too so they can explain why an image might look the way it does.
All the best!
Annie