Canon T3 or any of the Panasonic compact systems.

I am always very frustrated with the quality and zoom of the pictures from my Lumix P&S. I want to be able to take pictures of the family and adventures. I also would like to start taking more nature photography. I know that I want a Compact System (SLR-like) or a DSLR.  I cant spend over $600 so I cant spend a lot on the body without it including a lense. Sams Club has the T3 with 2 lenses and a case for $599.  I like the idea of the SLR like ones because they are smaller and lighter and simpler to use. This needs to be simple for me or I wont end up using the camera. I want to be able to have a very good zoom, take videos, and take action shot of the kids playing sports.