Safety should be their first concern when photographing your child. Do they use an assistant to ensure your child's safety?
They must have a lot of patience. New born photographers work on the baby's time schedule, not our own. So your photographer should allow enough time for you to feed and comfort your child whenever necessary.
Prints, Digital or Both?
When you print your images on your own computer or at a one hour place, the color balance may be off, they may be too dark, or too light. The best way to ensure you will have beautiful images in your home is to let the professionals take care of it for you.
Save your digital files for archival purposes.
Your new born will only be this small for a very short period of time. Make sure the images you have to remember this time are beautiful. It's kind of like a wedding, you only get one chance to get photos of a two week old. Once you get your images back, you can't redo them if they are not the quality you want. Choose wisely.