Things you don't need:
Baby Bath - I took baths with my baby. I didn't have to bend over and my girls never cried when I was in the bath with them.
Swings, Bouncers and Exersausers - A baby blanket works just as well. Selena did LOVE the swing and it was really nice, but Allie could take or leave anything. But really a simple blanket with a few rattles nearby worked pretty good.
Crib/Bassinet/Pack and Play - I know most people would not agree with this at all, but Allie has always either slept/napped in our bed, on a mattress on the floor, or on a blanket on the floor, or while being held (in a baby carrier). I tried having Selena sleep in the crib, but I couldn't convince myself it was right and it stressed me out, so I didn't even bother with Allie. It worked out well. It is a lot easier to lay a sleeping baby down on something that doesn't have a rail in the way.
Nursery - If you aren't going to do a crib, you don't even need a nursery. You just need to find a place to put their clothes and diapers.
Push Walker - An upside down laundry basket works better than any of the fancy toys that kids push to learn how to walk. With a laundry basket they can cruise around it to push it another way and turn it.
Stroller- If you have a good baby carrier, you really don't need a stroller. I mostly just used the stroller to carry stuff with when I was out. Not having a stroller can be super convenient in that you don't have to look for ramps or elevators.
Fancy Breast Pump - If you are going to be working and breastfeeding then this would be a must, but if you are planning on staying home the only time you would need one is if/when you want to go out and leave your baby with a babysitter. I had an Avent Isis hand pump and it worked just fine when I needed one. I even used it for a couple months when I was working part time right after Selena was born.
Things to Cut Back On
Onesies - Yes they are adorable and you probably need quite a few, but usually these are something that you have way too many of.
Bottles - If you plan to breastfeed and stay home you really only need one or two. Even if you bottle feed and stay home you can get away with just a few by washing the bottle right after each feeding. If your child will be going to day care you will probably need more.
Bibs - This kind of depends on the kid. If your baby is especially drooly a lot might be nice, but for eating all you need is to get one Baby Bjorn bib and you are set.
Blankets - Two or three LARGE sized swaddling blankets. They can be used for swaddling and setting baby's on the ground.
Toys - Buy a nice set of wooden blocks and you are set. Supplement with bowls, spoons, and measuring cups when they are young. When they are older you can make all sorts of toys from cardboard, or paper (origami) and when they get tired of the toys you can just toss them in the recycling.