Here are my adds to the good advice already here. Don’t get too caught up with buying baby things. They grow fast and what they truly need is you, food, and sleep.
If you can afford the initial sped to get cloth diapers they are amazing and will save you and the planet a ton.
On that topic a blanket I the floor is the best changing table for money and safety. The kid can’t roll off the floor.
Be there to support the mother. This can be a difficult time especially if she is breastfeeding. Sleep will be difficult for both of you but especially for her.