At three weeks they tend to sleep a lot and don't move much when they are awake. You will find in the coming months and years that this will change rapidly! Use whatever shutter speed you need to keep the ISO low. Depending on the amount of light you may need to use your tripod and either the timer or a remote cable release to prevent camera shake.

For the newborn I would go for the 50mm f/1.8 lens and use a wide aperture like f/2 or f/2.2 - wherever the image sharpness improves from the normally slightly soft wide open f/1.8 on most of those type lenses. Focus on the nearest eye. I'd try to set up a spot in a neutrally colored room (white or light gray walls) with a window that receives direct sunlight, but place the baby in a spot that is only getting diffused light from the window.

When photographing newborns the perspectives given by using closer shooting distances aren't necessarily bad. With most other people close shooting distances result in goofy looking distortions. But with a 50mm lens on an APS-C camera when shooting babies I've not found this to be the case. If you do find the perspective of tighter shots using the 50mm lens to be a little odd looking, then back up and use the zoom lens in the 80-105mm range with the aperture set as wide as it will go.