When my boy, now 2 years old, was just about to be born, I wanted very badly a 24-70. I purchased one used, but in excellent condition, 3 days after he was born. I know this specific lens is outside of your purchase budget by about 3x, although I will say it's now my favorite lens of all my lenses. I have a 7d crop camera.
What I have found is, I very rarely use less than, say, 45-50 mm focal length when photographing portraits. I just don't like the wide-angle distortion of people's faces. I will only use less than 45mm when photographing a small room of people only if I wouldn't get any photo at all by observing my 'don't shoot under 45mm' rule.
Even though people do the 'math' of, 'well, it's a 1.4 crop factor times a 35mm focal length, so that's right about 50mm....', that is not accurate. It's still the exact same distortion of a 35mm focal length.
So, to the point of your question, generically, I would not recommend any lens less than 45-50mm focal length, with a max aperture of smaller than 3.2, for the photographic purposes you stated. I don't know what specific lens that would be to recommend, but there it is.
For the time i was in the hospital, I honestly just used my cellphone camera and my Sony DSC-N1 snap-and-shoot camera. I used my DSLR after returning home.