It will always depent on how much into "it" are willing to spend. Shure having a single-all-in-one-flash-zoom is more travel friendly, when it comes to enjoying the results, I stick to the-bulky-camera-bag-full-of-stuff. I shoot sports for a living, so I would recomend DSLR. Now depending on what brand to choose, no brainer, Canon or Nikon. Besides the camera, it's important to chose good optics, so you can start with a body and as first choice a zoom 28-135mm to get you started. once you feel your new needs, and planning sports with kids, a 70-200mm 2.8 would be my next choice.
I would recomend getting one lens at the time learning how to use it, and then getting if needed some more.