Taking pics of my toddler, both action and portrait

Amateur in charge of taking pics of my little one!  I am improving my photography skills, but would appreciate a user-friendly, intuitive interface so that I'm not missing shots trying to set them up.  I have a Nikon Coolpix and it's just too slow to capture pics without a blur, and so slow to shoot in natural light situations that at times, I miss the shot altogether. I would also like to be able to manipulate more to capture a shallow depth of field to focus on getting more beautiful portraits of him.  So I'm torn between the wider aperture and shooting speed of the xz1 versus the better image quality of the lx5.  I don't do any post-processing at this point, but I can see where in time I might develop this as well. I would appreciate advice!