The items I've listed aren't neccessities such as diapers and a layette but they've definitely made our life with a newborn a little simpler.
1. Fisher-Price Rock 'n Play Sleeper - this was awesome with our firstborn who suffered from acid reflux and needed to sleep reclined. It's also extremely portable and moves easy from room to room (even the bathroom while mama showers).
2. Halo Sleep Sack. - the hospital our babes where born at uses these and we picked one up for ourselves as soon as we got home. They keep baby nice and warm and there are no loose blankets to worry about.
3. Itzbeen baby care timer - get one of these or download a baby care timer app. You'll thank yourself for it in the middle of the night when baby wakes up to eat and your too sleep deprived to tell the minute hand from the hour hand let alone do the mental math to determine how long it's been since the last feeding.
4. Sleepy Wrap - babies want to be held all the time. This is perfect for the little one and I can have my hands free for other tasks (like chasing a toddler).
5. Nursing cover - babies get hungry while in public places. I'm much more comfortable discretely nursing in public than having people in a restaurant glare at me for not quieting my screaming hungry baby.