Hi Kate,
Since you are a beginner in DSLR photography and it seems you have a budget, I would recommend the D3100. I purchased the D3100 over a year ago for basic photographs but have noticed that the camera is more powerful than you might think. The D3100 is a great first DSLR and has the speed and autofocus capability that you need to capture those special moments. The size of the camera would be perfect for you as well. You could be holding the camera with one hand and have control of all the necessary functions. Overall, this camera would not disappoint you with what you expect to do with it.
Here are some quality examples of what the D3100 is capable of:


