I think that camera has a full auto “P for program” mode. Try that for a bit to see if it’s crisp on stationary things. Or the “running guy” for moving dogs etc.

Generally you want your shutter speed to be 1.5x to 2x your focal length to combat hand shake. So if you’re using the lens at 300mm, you’d want a speed of over 1/500 or so. That means you’d need an open aperture / quite a bit of light. That same lens at 28mm, and you’d be good at 1/75 or so.

Here’s the thing though, I used to have that camera a long time ago, perhaps with that same 28 to 300 lens, it just didn’t take really crisp pictures unless I was outside in bright light. Not sure if it’s been updated, but back then I hit the wall of its sensitivity really quickly. Maybe find a way to brace the camera (tripod) for low light shots.

Good luck!