I am in no way qualified to give any 'expert' advice, but with a seven month old Grand-son, I can certainly inform you of some of the problems.
First, and probably most important is that for the first few months, the baby will always be either lying down or being cradled. This makes it very difficult to aviod your photos looking 'samey'. At least with the cradled shots you can get the lighting reasonable by moving the baby into better light, that is near a window, or outside etc. The backdrops you will be using initally will be Mum's cardigan. The baby will be well wrapped up most of the time for the fist few weeks. however, you will probably be able to use the blanket, or whatever the wrappings are as a background if you crop nice and tight.
Second is that you will not always want to use a flash indoors, so make sure that you have your white balance set correctly, or bracket the WB.
If you are going to use a flash either diffuse it or bounce it. Much like any portrait use, really. gives a nice soft light with no harsh shadows. I use the built-in flash as a fill by having it set to minus EV of varying strength.
Third, tight cropping is where you will probably get the best shots of the baby. You can do it with either good framing with a zoom lens or in processing. (not a good idea to get the camera to 2" from the baby). However, you are going to have to make sure that you get some pictures of the other family members. You know, here's one of great Aunt Matilda holding little Jack (or Jill). In these pictures they might as well be holding some fish and chips because of the size of the nipper, and it will be wrapped up!!
Things will get easier as the baby gets bigger. Although I would not hold up any of my photos as being an example of how to do it, you might like to have a look at the pictures of Oliver in the 'People' section of the members gallery, and the oliver album in my albums.
HTH