Advice for introducing pets to new babies?

So we know the pets think something is up. There are all the new nooks and crannies in the baby room. There's swing in the living room with dangley toys. There's a bassinet in our room that the cats think is really snugly. There's less room in the car because of the seat. Layla, Piper and Cracker all like to sleep on my belly. Piper even thought it would be funny if he jumped from the ground on top of my belly, as if it was his personal shelf. If anyone has any helpful advice as to how to introduce pets to new babies, I'd appreciate it. We have a hyper dog and two lovable cats, who might like to get a little too close. Friends have told us not to do anything too different, but only allow them in the room when I am in there. Also, someone mentioned bringing home a baby blanket from the hospital so they can be introduced to her smell before we get home. Another friend. I think it will be fine, but I don't want our first love to think we don't love them anymore once our new love arrives.
Layla relaxing on my belly, curious by the movements.

Piper and Cracker hanging out in the bassinet after Grant put it together.