Thanks all for the advice. While I do expect my new addition to be a key subject I like to shoot just about everything right now as I try and learn, I had thought of the 70-200 as a highly versatile lens to add to my kit but in reading the above I am rethinking that and looking at my 50mm 1.8 as a possibly good starting point. I will look into something like a 50 1.4 or 35 1.4 as I do shoot on a T3i so its a crop although I have never been able to get comfortable on primes as of yet, maybe a good time to learn as the baby will lie around for longer than I care to shoot I am sure, at least for a while.
Another avenue to consider is adding a flash if you are worried about indoor/low lighting conditions in which your subject won't be stationary. The 430EX or 580EX flash can breathe new life into your lens collection. You might be amazed at how a little bit of bounce flash can benefit indoor shooting, even when using a large 1.4 or 1.8 aperture.