What do you really need for baby?

My dad has always teased me for being a minimalist. My husband, on the other hand appreciates the trait, because it's saved us a lot of money over the years! If you have kids already, its pretty obvious that there are a lot of unnecessary baby products out there. Since I've already done this once with Layla, I'll share what we decided to acquire for our second baby, and how we saved money on what we did buy.
This list is probably adequate for the first 6 mos. or so, then your list for safety items especially will vary depending on how your house is laid out once baby gets mobile. 

Clothes:
As you're buying or looking through hand-me downs, make sure you select clothes that will be season appropriate. For example, if you're due in January (winter here in the northern hemisphere), your 12 mos. outfits should be winter weather appropriate. For the first 6 mos. or so, keep most of the outfits comfortable. Since babies aren't really getting around at this point, don't have more than a couple stiff dressy outfits for pictures. Most babies hate them! You'll probably end up changing your baby back to a sleeper right as the event or picture session ends (at least that was my experience).  
The core of your baby's wardrobe should be onesies and sleepers, with more sleepers if the weather is cool.
For the newborn size, I think we ended up with around 7 sleepers and more onesies, which is more than adequate since they spend so little time in this size. We have more 0-3mo. outfits, with probably closer to 15 ourfits and more onesies than that. Most of our clothes were gifts or hand-me-downs.

Diapers:
Last time we ended up doing mostly cloth, so that's the plan this time as well, but I do like to use disposables for travel, or for babysitters who don't like cloth. We started this time by going to a local resale shop and stocking up on covers and prefolds, as well as a few all-in-one diapers (these are more expensive). We spent about $80, then got a few more prefolds and covers as gifts. Some of the smaller covers will only fit until he reaches 13/14lbs, but they can be resold at the same shop, so we can use the trade in value to buy bigger covers! The prefold diapers can be used with bigger covers, so you only need to buy these once. The only caveat is that you will need some smaller inserts or thinner prefolds for just the newborn stage. Some people just use washcloths or the inserts from pocket diapers. Another option is to use disposables until baby reaches about 10lbs and the prefolds with covers fit better.
My husband is not a fan of cloth wipes at all, so we plan to just buy disposable wipes. For the messy diapers, I suggest just rinsing baby off in the sink rather than using 10 wipes to get the job done!
I think that cloth diapering works best if you only have enough diapers to last 2-3 days at the most, that way you won't procrastinate on washing them. The covers can often last through a few changes, so if you have 10 total in each size that should be more than enough. I managed with only 5 covers when Layla was small, but ended up handwashing a cover and using a blowdryer more than a few times!
You also need something to soak dirty diapers in until washing. For this, we got a couple detergent buckets from a neighbor. Since we have 2 bathrooms now, we will have one upstairs and downstairs. Don't waste money on a diaper genie! Any bucket/large container with a lid will work just fine! I like the container or bucket to be small enough that it can be dumped straight into the washer.
A waterproof pad or travel kit for diaper changes is also handy.

Bathtime/Health:
Thermometer-This is one item I would buy two of, simply because a high fever can become dangerous quickly for a young baby and you don't want to discover that the battery is dead just as your baby is sick.
Nail clippers-I found that regular ones work fine for a baby. The baby clippers with the plastic guard were actually harder to use because they're so bulky at the top.
Soap-You can use something designed for a baby, my favorite here would be something like Burt's Bees baby wash, or another brand that doesn't have perfumes or sodium laurel/laureth sulfate.
Babies need less soap than you think, and their skin can get dry if you're sudsing them up all the time! I wouldn't use soap on their scalp more than once a week.
Raw coconut oil-This is seriously good for so many things! I used it both as a diaper rash cream and for any cradle cap or dry skin areas. I liked it better than any lotions out there, and it doesn't have any chemicals or scents that your baby could be allergic to. It also absorbs into the skin better than liquid oils, such as olive.  
A baby bathtub and towels are nice, but not really essential. I did like the thin hooded towels better because our regular towels are really bulky. We got a bathtub for free this time, but if we hadn't, I would have probably skipped getting one.

 Sleep:
Last time we had a crib handed down to us, but ended up mostly co-sleeping, so we just got a Pack-n-Play with the bassinet insert this time. It will be right next to our bed, then we will probably move him to his own room once he's 6 mos. old or so. Specifically marketed co-sleepers that attach to an adult sized bed are also nice, but the Pack-n-Play is much cheaper if you end up buying new.

Travel:
Baby carrier-These are a must, especially if your little one tends more toward being fussy. This time we have a Moby wrap and an Ergo, both of which can be used from birth until at least age 2. The Ergo needs an infant insert if you're using it for a baby under 12lbs. Some people also like slings, but I prefer a carrier that disperses the weight more over my hips and both shoulders evenly. Layla lived in the Moby until she was 2!
Carseat-Don't waste the money on an infant-only seat! Most convertible seats are designed for 5lbs and up, which means you can use a single seat from birth until around age 3. I would just recommend an infant head support for the first 6 mos or so. Carrying a baby in the seat is horrible for your back, and since you should already have a carrier, its easy enough to pop baby in there as soon as you get them out of the seat.
Remember, current recommendations are to keep your baby rear-facing until age 2, and always remove bulky coats or snowsuits before strapping baby in!
Stroller-I would highly recommend buying used again in this category. Strollers are relatively easy to find cheap when they're used, but are quite expensive new. I didn't use one right away, but they are nice for the city dweller who likes to walk to the grocery store with baby and doesn't want to use the carrier while toting several bags of groceries!If you will be storing the stroller in your car, using it on public transit, or flying with it, make sure it is lightweight and folds small enough to handle easily.

Feeding:
If you're breastfeeding, it is still helpful to have a couple bottles and a manual breastpump. Unless your baby will be in someone else's care for quite a few hours each day, you probably don't need to invest in a double-electric pump. However, if your health insurance will pay for one, I highly recommend it!
Pacifiers-Many people have a love-hate relationship with these. I didn't plan to use one with Layla, but when she had doubled her weight in 2mos and still wanted to nurse constantly, it saved my sanity! Some current research also supports pacifier use as beneficial to the breastfeeding relationship. I would definitely say that a pacifier is preferable to a thumb because it is more sanitary, and can be taken away whereas a thumb is always available. Pacifier clips are also handy, but I only liked the ones with a metal clip because the others would never stay attached to baby's clothes.

Comfort:
Swing or bouncer-We got both of these as hand-me-downs this time, so only $20 total was invested. Since the covers can be washed, I would highly recommend used. You may find that your baby doesn't like the type that you bought, so it makes more sense to try something out from friend or neighbor rather than investing a ton of money. They are also making more swings that use electric rather than batteries again, which will save money in the long term. This item isn't truly essential, but it is nice to have a safe place to set baby down, especially if your home has more than one floor. We plan to keep the swing downstairs since our bedrooms are on the second floor. 

Things you don't need:
Wipe warmer
Infant carseat
Shoes (worthless until they can walk)
Diaper bag (just use a backpack or large purse you already have)
High chair-I prefer the space-saving type that straps onto a regular chair. Plus, you don't need one until around 6mos when you introduce solid foods.
Changing table-I found that the travel changing kit/pad was more handy since I preferred to do changes wherever I was at the time.
Burp cloths-Cloth diapers double as cleaning rags for whatever messes might occur!

Let me know what your essentials and non-essentials were!