Once you pick up the essentials for your newborn and all your essentials for breastfeeding you can start thinking about the things that are pretty good to have as well...
A reclining umbrella stroller. I never had one of the big stroller/car seat combos and didn't miss it at all. I had a universal infant car seat stroller with my first and it was really great to have. After the first few months or so we only used our umbrella stroller. I haven't used a stroller at all yet with this baby and she is 4 months old, so you decide. If you do a lot of walking or jogging you can consider getting something three wheeled with air filled tires. This is a great website for reviews. Most jogging strollers don't recline so you can't use then at first. Make sure they'll fit in your car before you buy them!!
Play Mat
. My girls always loved laying on these and looking at the dangling animals. Lots of entertainment. All of the girls have been in love with the lion and giraffe in this set.
. I highly recommend getting a swing if you can. It helps some babies fall asleep and it makes other babies happy. Rarely do babies hate swings. I love the cradle swing because it reclines a lot and can be adjusted to more of a seat. More importantly, it can swing from side to side or back and forth. I've also had a swing that is a bouncy seat/swing combo but I wouldn't recommend it. It does save space but I'm not a big fan.Baby Monitor. I use these a bit with my kids. I've never lived in a place that I couldn't hear babies on the other end of the house but if you go outside to the yard while one is sleeping you'll never hear without a monitor. Check reviews online when deciding which one to get. Make sure it is a different frequency than your cordless phones or any wireless router you have in your house. I have one that has sounds and lights up with noise and I like it a lot. It isn't available anymore but it is a First Years brand and is still working well. It has some rubber on the sides of the receiver which has probably kept it from getting broken since it has been abused slightly over the years. The video monitors aren't necessary but if you want one, go for it.
Pacifiers. Buy them right before baby is born and don't open them! Keep the receipts taped to them just in case you don't need them and need to return them. After baby is born you may want them and some kids want to try out a few kinds to find what they like. We like MAM around here. They come in different sizes so make sure you get the 0+ ones and then when they turn about 6 months old get the bigger ones.
A crib. Even if you are going to co-sleep, you might want baby to take naps in a crib. OR, you might get a baby that isn't a fan of co-sleeping, which can happen! You may want something in your room so baby can sleep there for the first few month. You can also use a mini crib or Pack N Play, or a Co-sleeper, Mini Arm's Reach Co-sleeper, or a Close & Secure Sleeper. Of course, there are bassinets as well. It is really up to you. Check them out, see what you like. Remember that bassinets are outgrown within a couple months usually. If you use a Pack N Play it will have more longevity but it isn't that comfortable. We used a mini crib and loved it. Daphne slept in it until she was 1 because Naomi was still in the full sized crib. The mattress that comes with those is usually very thin so think about buying a better one. Whatever you do, try out some cribs in a store to see what features you like best. If you want one that has a drop side, what kind do you want, etc.
Crib Sheets & Mattress Pads. No matter which way you go as far as a crib or bassinet goes, you'll need waterproof mattress covers and sheets. Get at least 2 waterproof mattress covers and 2 sheets. Accidents happen at night and you'll want to have a spare in case you need it. Spring for the fitted kind of waterproof pads if you can. There is a lot of debate about crib bumpers and I am of the opinion that you don't need them and they are dangerous. If you absolutely must have a bumper, get the Breathable Baby Crib Bumper
.
Rocker/Glider. Not mandatory but nice to have.
Blankets. We like to use blankets on the floor or couch when we lay babies down. This helps protect the floor AND the baby! They are also good for in the stroller and car seat. Beyond quilts and lap blankets I have enjoyed having Bundle Me blankets. They come in different sizes, colors and styles.
Clothes. Babies go through a lot of these. If you want to go beyond my sleeper and onesie recommendation, don't go nuts. Most babies will grow out of the 0-3 month size well before 3 months.
Changing Pad. These are handy whether you have an official changing table or not. This cover is the best, so soft and cuddly. I have others but this is by far my favorite.
Waterproof changing mats. I have a few of these and use them a lot. They are great in diaper bags or when changing baby on the floor or a bed.
Baby bathtub. Bath thermometer. 
I had a bathtub with my first two and can't find it now. I wish I still had it, they are useful but a sink will work fine for a while. I miss the tub now that Maggie is getting bigger. A thermometer isn't necessary at all but I had one and was surprised at how warm I liked my bath water! Too hot for babies! Baby temp was colder than I had guessed.
Sleep Sacks. Love these. We use them after babies stop being swaddled (sometime between 4 and 5 months for us) until they are in a big bed. Skip the smaller sizes because they aren't necessary.
Miracle Blanket. Babies are wiggly. Most babies will learn to break free from a swaddle before they are ready to sleep on their own. You don't NEED these, but they've helped my kids sleep much better.
Head support. Most car seats and strollers are not made to support babies heads correctly. You could always use a rolled blanket or let baby's head wobble but I like these.
I'm sure I missed things that are handy. But, like I said, none of it is absolutely necessary! What else would you add to this list? What would you take off?
