Newborn must-haves (0-3 months)
Rock N Play (or some other portable basinet) - I took Hayden's into the bathroom while I was showering, and he could lay next to the table while we were eating, and then it's what he slept in by the bed. You could also have baby hang out on the floor on a blanket. With a dog, this wasn't viable for our family.
White noise (phone app or an actual machine) - miracle worker for soothing babies. Alternative: Saying "SHHHHH" for a long, long, long time until your tongue is numb and you have spittle flying from your mouth.
Sleep sack - the kind that wrap a baby's arms in so they don't scratch themselves in their sleep (plus, they like being cuddled up tight). You probably won't use these until your baby is about 1-2 months old, but we used ours even when Bubs was itty bitty.
Good swaddling blankets - some people swear by the muslin ones, but they're pretty expensive. Flannel ones are hard to swaddle. We found stretchy blankets like the ones they have at the hospital were pretty inexpensive and stayed wrapped for the longest time.
Night light - so when you're up in the middle of the night, you don't blind yourself and the baby. My phone just didn't cut it as a nightlight. We had one of those nightlights that projects the stars on the ceiling. This was also helpful for changing a diaper in the middle of the night without waking the baby up too much.
?Little bottles and big bottles - even if you breastfeed, the little bottles are nice for when daddy or grandma takes over for you so you can pump/nap. It feels ridiculous to put 2-3 oz. in a 10 oz. bottle. There are lots of mommy debates out there regarding introducing infants to bottles, so this one is on the maybe list. I'm not sure what your philosophy is.
Black and white toys/books - when someone gave me black and white toys as a baby gift I was like, "whaaaaa?" - these were the first toys that caught Hayden's attention because babies see sharp contrasts before they can see colors.
Boppy/nursing pillow - this will save your arms from having to hold baby for hours while nursing/giving bottles. Also good for propping up babies for cute pictures.
Nursing cover - for when visitors are over (also, get lanolin for the girls).
All-in-one carseat/stroller/baby carrier - So you don't have to get baby in/out of the carseat when you're shopping, running errands, actually being social, etc. Depending on when you have your baby, it's also helpful to have something to cover the carseat when you're walking into a store and stuff. In windy climates, blankets don't cut it, so we got a zip-around cover. Note: educate yourself on what is/is not appropriate for car travel. Don't get a cover that you put in the inside of the carseat under the straps. The packaging on these warns that they're not for car use.
?Pack N Play - I have this with a question mark because we didn't use ours frequently. We had the Rock N Play that we used constantly. However, when my aunt started watching Bubs, she used this for taking care of him and loved it.
Baby soap/washcloths and baby towel - Unless you want a dirty baby...Around when Bubs was born, Johnson & Johnson got their license taken away for putting carcinogens in the baby powder/lotion/something like that. I used carters or whatever smells good in the organics section.
Clothes - of course. Stuff for layers, even in summer!
Baby-safe stain fighter and laundry detergent - for all of the yellow poop that will soon be in your life, and in your clothes, and in your baby's clothes, and maybe on the door, the carpet, the dog, etc. Note: dark clothes don't show poop stains :) We really liked dark clothes we got and Bubbs wore them a lot. We felt self-conscious when he was out-and-about in stained clothes and baby poop stains are hard to get out.
Books or something to keep you entertained - for when you are nursing/feeding baby/can't sleep because you want to make sure (s)he's still breathing.
Bibs - Around 3 months, Bubbs started teething, so it was drool-central in our house. If we put a bib on him while he was awake, we didn't have to change his outfit a million times during the day.
Nursing bras, nip coverage, and granny undies - get bras that are comfortable, and something to prevent leakage from showing, and granny undies so you don't ruin your good ones :)
?A GOOD breast pump - I bought a little hand-held one. OMG OUCH! Shell out the couple hundred bucks for a good quality one. Also, avoid buying used off of Craigslist. Even if properly sterilized, the former pumper's milk amoebas are still floating around in there. If you get used, make sure it's from a family member you trust completely.
Meh for Newborns
Baby wearing things - I tried the Moby wrap and we had a Baby Bjorn and there were a couple other baby carriers that I tried and returned. It was pretty difficult to get a baby in the wrap by myself and Bubbs wasn't a big fan of them. I was worried the few times he fell asleep in them that he would suffocate. With that being said, I will probably use one of these for baby #2. They're easy for carrying a baby around while you're doing stuff.
Baby tub - you won't need this until around 1 month since babies can only get sponge baths with their umbilical cord. You could just as easily give a baby a bath in the sink, though.
Changing table - I know a lot of people who just change their babies on the floor. No chance of baby rolling off anything. However, with a dog, this might be difficult unless you go in a room and shut the door. We used a changing pad until Bubbs was about 6 months old and started trying to roll off the pad. Now, he is exclusively changed on the floor.
Swings - some people swear by them, other parents say their babies hated them. Bubbs was okay with his swing, but he didn't like being left in it and got bored with it after about 5 mins or so.
Burping cloths - this is probably personal preference. I had a friend who just wiped up spit-up with blankets. We used bibs. We didn't really carry around burping cloths. Every now and then, they were handy, and it was nice to have them in the diaper bag.
Stocking up on diapers - I know far too many babies with allergies to certain diaper brands to recommend stocking up on diapers. Don't use your gazillion coupons to buy 20 boxes of Pampers diapers only to find that your baby's bum is on fire whenever you use them. Yikes! The supply of diaper coupons is not limited and you will get more.
4-6 months+ must-haves
Feeding Chair - Andy and I started with a high chair, but we have a small kitchen and it was kind of awkward feeding Bubbs while he wasn't at the table. We sold our high chair and bought a 3-in-one booster seat thing that you strap into chairs. Perfect for when we want to go outside and eat on the patio or go to a friend's house.
Spoons, sippy cups, plates, snack containers - for when they're eating finger foods (10 months+ :)
Night time diapers - We switched to these at night when Bubbs was about 14 months. We change his sheets way less often.
Crib and crib sheets - for sleepy babies :)
Meh for 4-6 months+
Baby puree blender - you don't need a baby bullet or anything special. You can use a blender and it works fine. (And actually, I'm pretty sure the baby bullet has been recalled for containing lead or something like that)
It's been a while, so I might be missing a thing or two, but this should be a pretty good start. Baby stuff is so expensive! Let me know if you have questions on recommendations. Andy and I played around a lot with the things in the stores to make sure we liked them. Nothing sucks worse than buying something expensive, only to realize that you hate it because it's hard to collapse/isn't portable/is the wrong height or what-have-you. This is how I ended up with 3 strollers and why I sold our high chair on craigslist.