Keeping in mind that I am a
diva, here are a few baby products that I recommend to the new mom just starting out and making her way through the overwhelming amount of
junk baby products one needs for your soon-to-enter baby divo/a. My first bit of advice is to make a registry at Babies R' Us or Amazon: make other people buy useful items instead of endless arrays of 0-3 month clothing.
Alright, now that we know you're not footing the bill, you should buy the most expensive items out there, right? Well, in my experience, the answer is "kind of." There is a price point that generally reflects ill-made equipment and then there is a price range that reflects quality. If this is going to be your only child, perhaps you can get away with being el cheapo/la cheapa (my husband is a Spanish teacher, can you tell?), but if you are planning on having more than one baby, I would recommend looking at higher quality as to save yourself money in the long run. Of course, I am a huge advocate of hand-me-downs, but just be aware that there are certain baby items that should not be handed down due to safety considerations. Be frugal but protect your baby first!

My first recommendation is a smaller item, but a life saver for breast-feeding Mommas.
Lansinoh Lanolin nursing cream 
is an absolute must-have if you plan on breast-feeding your baby. Sorry Ladies, I guess your mom forgot to tell you that breast feeding hurts sometimes. This is true especially at the beginning and especially if you give birth to a chunky monkey like my Noah who likes to eat and eat. This cream literally made the difference between me crying and nearly switching to formula to being cheerful and proud to feed my son. Bring it to the hospital with you and keep it by your bedside. This will also help breast-pumping moms.
My next recommendation is a
slightly larger purchase: a stroller travel system. This means a heavy-duty stroller (umbrella strollers = pain n' neck) and a car seat. I strongly urge you to consider
Graco's line of Quattro Travel Systems. 
I prefer these systems because the car seats are hard-core and will hold babies rear-facing until they are 30 lbs. while most only hold up to 22 lbs. My son still fits in his rear facing car seat and he is nearly 17 months (and a big boy for his age). Also, the stroller is made of remarkable quality and easy to push in all sorts of terrain. You can certainly purchase a much, much pricier stroller system than this, but my recommendation is to go middle of the road with this item- not too cheap, not too (unnecessarily) expensive.

My last recommendation is an obvious one, but I think important to mention. Noah is a
Pampers
baby (no, hippie friends, I did not attempt cloth). At birth, I had all sorts of diapers given to me for testing. I tried Luvs, Huggies, generic Walmart brands, and Pampers. Pampers won hands down, no questions asked. I admit,

they are more expensive. But, I didn't have to change his clothes when he had a poop explosion and I didn't have to worry about leaks. Furthermore, I could leave Pampers on him longer because they were more absorbent and thus he used less of them. If you register for diapers, don't get a huge box of newborns, as your little one most likely grow out of them pretty quickly (unless baby is premature). I would, however, recommend registering for one large box each of sizes 1-3 to start and then asking for more as presents because, trust me, you will use them.
I know a lot of you may disagree with what I have recommended, but I am sure my soon-to-be first time mommy readers would love to hear your recommendations. What diapers do your children use? What kind of strollers and/or car seats do you recommend?