I would buy from a place with a good return policy! Then if you don't like it you are not stuck with it.
If you are going to take pictures of moving targets, kids-dogs-etc, it is going to be more of a challenge with a cheaper point and shoot style camera. They take a second to focus and in that second the target will have moved. If you focus on a certain place (say on the lawn for an example) and wait for the subject to run in to that spot you might have better luck.
But, I would look for a camera with the best Optical zoom, digital zoom is what you can do after on your computer when you crop the image.
And as always, I would stick with a bigger name in cameras, I have a panasonic-lumix I keep in my purse, it even does video.