Just so you know --- you don't really need more stuff in your house. IMHO, I think baby essentials are diapers, breasts and a safe place to sleep. All the rest just makes being a parent easier.
Here is a list of our top baby items. They are in no particular order:
1. Sling for carrying the baby. You may want to try a variety of slings since you don't know what will work for you and with your baby. Also, different slings and baby carriers work at different ages of the baby. Our favorite sling is from Kangaroo Korner and it is called the "adjustable fleece pouch." When your baby gets bigger, and you don't want to carry the weight on one shoulder any more, try the Ergo Carrier. I find this carrier extremely comfortable and my twins love it (one at a time of course).
2. Pure lanolin (brand name I used is Lansinoh) if you are going to nurse your baby. Buy the smallest tube available because it lasts forever! This product is wonderful at helping soothe the nursing mother.
3. Breast pump (again if you are going to nurse your baby - which I highly recommend). Don't get a hand pump - it is not worth the time or energy! Electric breast pumps are very efficient which as a mother you will appreciate. I used a Medela Pump-In-Style which worked great.
4. Fleece car seat insert to keep the baby warm without messing with blankets. We used a Bundle Me which we really liked.
5. Lots of blankets for swaddling the baby. Swaddling new babies helps them to feel secure (like the womb) and helps them not startle themselves awake. The ones we liked the best were waffle weave which are a little stretchier than flannel. You may also want to check out a book - The Happiest Baby on the Block which has great tips for settling a baby.
6. Hylands Colic Tablets - a homeopathic remedy for colicky babies. Nice to have on hand. The Hylands Teething Tablets and Gel are great for when babies start teething as well.
7. The Baby Book by Dr. Sears. This is a nice "how to" for new parents. It has simple information such as how to bathe your baby or monthly milestones. I really love this book.
8. A bouncer is a nice tool to have when you need to have your hands free (i.e. while cooking dinner). Some parents I know have one on each level of their home. I like the simpler bouncers the best. We used one similar to this. One of our children, in particular, was really soothed by the vibration mode.
9. 3-D Activity Gym - you put your baby on the floor under this and the baby looks at it and plays with it. We had a red, white and black one like this where the kids did their "tummy time." Remember, babies don't see colors at first - just contrasts so red, white and black are best.
10. Lactation consultant!!! If you are going to nurse, I cannot stress this one enough. Nursing is not innate (which is what I thought). It is a joint learning process between you and your child. A lactation consultant can really help set you up for a wonderful nursing experience. If possible, get a recommendation from a trusted friend.
11. Cod Liver Oil. Taking Cod Liver Oil when you are pregnant makes your baby smarter. We use this tasty one (no really) that is lemon flavored. For more information on this topic, check out W's blog post on the topic.
If you go here, you will find a list of W's dad recommendations which includes the post on Cod Liver Oil.
I am recommending these products and books because I have had good experiences with them and not because anyone paid me or otherwise coerced me to post.