Furniture, diapers, toys, food, car seats, and clothes. New parents usually don't know what exactly they need when the baby arrives. Here's what I used and what I didn't.
First, most general advice: do not overspend. It goes for your effort as well as for your money. No need to sacrifice your sleep for the sake of teaching baby sleeping independently. Hand-me-downs are OK -- new things will look just the same after the first couple of washes. No need to get all new baby furniture set unless you want one yourself -- baby will not know the difference. Pick your battles.
I stayed at home with all three children and never had a babysitter. It wasn't on principle, but I mention it because certain aspects of my experience will not work for others. For example, my children never had a bottle or pacifier, and I never learned to collect and store milk; also, I had no responsibilities but my home and children, and so I could afford some sleep deprivation. Of course, I didn't like it and tried my best to get enough -- and I learned that having the baby next to me at night was the best way. So, you possibly do not need a crib for a newborn.
You will need: diapers. You will do fine without a changing table -- a padded vinyl blanket (usually comes with a diaper bag) or a disposable pad from the "incontinence" section in a drug store will work well on your bad, on the floor, and anywhere you go. You will need baby wipes only occasionally, and for your own hands more than for the baby's bottom. Warm tap water will clean the baby more thoroughly, and less likely to cause rash. You will need oil to soothe baby's skin. Olive or apricot stone oil seem to be better than the refined frying oil, and better than special baby products in small overpriced bottles. Dove hypoallergenic soap is better than Johnson&Johnson and doesn't smell anything. You will want hooded towels. For other grooming purposes: small nail clippers or small scissors for nails; nasal syringe, non-sterile cotton (balls, pads or, cheaper, just bulk cotton). Do not use sunscreens until 6 month old.
You will need: a rear facing car seat. They recommend never to use one for more than five years. I'd say hand-me-down is OK as long as you trust the previous owner it never was in a crash.
You will need: something to carry the baby around. Get the baby sling in the color and pattern you like before the baby arrives, and maybe a front pack (and/or stroller). You will not need the back carrier until your baby can sit independently. Used front- and backpacks are OK, and used slings are virtually nonexistent. Speaking of strollers: in suburbs, get the foldable jogger with reclining back: it's easy to push and smooth to ride. My kids dubbed their double "an all-terrain stroller". It can be too big for shopping and public transportation. It costs $80-200, try to fold and unfold one before buying.
You will need: clothes. Babies can be sensitive to the synthetic fabric and to the detergents. Unscented Tide worked for my kids better than any special "baby soft" detergent. Babies grow fast and soil the clothes a lot. For a newborn, get at least 5 sets of cotton "onesis" (a tee-shirt with tails that snap between baby's legs), soft pants with elastic waist, and coveralls, all size 1-3 month or 6-12 pounds. Socks and hats are useful, shoes are pure decoration. Seasonal clothes: thin cotton receiving blanket to cover the stroller or baby's head from the sun, padded sleeping bag or a quilted coveralls for a cold weather, soft fleece and brushed cotton cardigans (pulling something over a new baby's head may be tricky). Fitted sheets for a crib or a basinet: there is only one crib-size standard, but at least two for bassinets. 2-10 flannel receiving blankets -- as blankets, as towels, as small makeshift pillows for different purposes, etc. Diaper bag: you will need a waterproof bag for diapers and baby things.
You will need: a place to put your baby to sleep safely. Even if you take the baby in your bed at night, you still will need it for naps. A bassinet or a large basket will do for the first three months. Get a water-proof mattress (and a water-proof pad for your bed, for the leaking milk as well as for the leaking diapers). Rocking chair for nursing is optional. I used to nurse the baby in the sling or in the bed.
You will want: toys. Safety rules for everything marketed as toys are pretty strict, but these approved toys may be unsatisfactory for a grown-up taste. Small baby starts to respond to the simple black-and-white face-like images very early -- draw them yourself and pin to the sides of the crib with paper clasps. Different textures include wood and metal, not only "velvety" synthetic and "furry" synthetic. Babies like chimes, bells and rattles. Safety approved plastic thing with noise will irritate you soon. My oldest daughter's favorite toy was a cubic tea-tin with several coins inside. It was red, cool, it rattled, and was fun to hold and shake. I took it from her when she started teething and biting on the tin. Speaking of teething, the clear plastic ring from the pharmacy was a great success. It is filled with water with quarter-inch stars or fishes in it, fun to play and can be cooled in a freezer to soothe the aching gums.
You will not need: baby food. I don't mean formula, but the small jars with mashed veggies and such. Not for the newborn, not ever. You can perfectly well mash boiled carrot with a fork and strain it with boiled water to desired thickness. You can feed the baby the same plain yogurt from the quart-size cup you eat yourself, and use the large jar of apple sauce for several days. Bulk organic oat bran is healthier and cheaper than instant oatmeal. Baby food is disgusting -- just risk to try it. Unsweetened Cherios can be useful as a finger-food later, and you still may want to buy couple of jars for jars themselves, to keep snacks.
See also: children, baby carrier, diaper, baby car seat, jogging stroller.