first time poster so apologies if it's too basic a question.
I've decided to invest in a good quality camera for the primary purpose of taking photos of my 2 young children. I expect a lot of the photos will be taken indoors and some outdoors, some portraits and some "action" shots of them running around.

I've been to a few shops for advice and the same 2 names keep on coming up; Samsung NX10 and Nikon D3100.
I would be happy with either but before I spend my hard earned I would appreciate some advice.
I've seen the Samsung at least 100 cheaper which is a consideration as it would give me money to spend on another lens. I know that there is a better range of lenses available for the Nikon but I don't envisage getting a huge collection.
So, I suppose I'm asking which is the best camera for my needs, and would the extra outlay on the Nikon give me a significant benefit?
Any advice welcome, I'm completely confused and going around in circles!