Clear and crisp action shots indoors or out.

I need to be able to play around with low and high light situations, take beautiful still shots of the family, etc but most importantly ... I need to get my kids in action... Soccer, Basketball, ballet, on the trampoline, laughing, playing and even throwing those tantrums- lol.

I have looked into the Nikon D700 and think I am in love but the cost and other features seem like over kill for what I am really trying to accomplish.  I have read reviews that compare the D500 to D700 and think that the Nikon D500 or D5100 could work for me.  I see the Cannon T2i's and see that I have more reading to do.  I need to know what people think is my best option... please feel free to add other models in your response.  I see the new sony looks amazing but again don't want to spend more if I am still not getting these amazing action shots!

Thank you

Brooke