Hi OP. Congrats! I think all the prior posts have been helpful. Most of what I suggest may be repetitive.
Bedding: I would get a new crib but not an expensive one. We have 2 we paid
$100 each that came from
Amazon, free shipping. They do convert to
toddler beds. Walmart.com also has inexpensive cribs. I would spend
money on a better mattress, something firm. Bumpers aren't safe so
just get some sheets and mattress pads.
Stroller: Used is fine here. I am not sure what area you live in and how much
stroller use you will have. My sister lives in NYC and I live in the
suburbs in Mississippi. Our needs are different. Pick what it best for
your needs.
Car seat: New. Infant seats are not a necessity but much, much easier. I
would get one and purchase a convertible seat later.
Feeding: Breast is best and least expensive. If you formula feed (and there is
nothing wrong with doing so) generic formula will save you a ton of
money. Buy a breast pump later after you are sure it is the method
you will choose (and get a good one).
Diapering: I know nothing about cloth but it is cheaper in the long run but most
day care centers will not take them. I buy Luvs or generics for day
use and use the good ones at night. Use coupons, check with
amazon for their amazon mom and subscribe and save, diaper.com
can be pricey but does specials.
Bathing: Nothing wrong with the kitchen sink and then an inexpensive tub later
Toys: Used is fine. I cleaned ours with bleach and water or usually, vinegar.
My boys used their swings a ton, bouncers a ton, and exersaucer things
until they were way too big. I also recommend a pack n play. Great for
securing a baby in while you clean. Used is likely fine, or get a basic
model. We have a $69 one and a $200 one. The cheaper model is just
fine.
Clothing: Check yard sales, consignment shops, good will, etc. Used is fine.
I find that unless I have a coupon that most everything I can buy off of Amazon will be less expensive than at babies r us and those type of stores. I primarily use them to look at items but very rarely do I buy from them. My boys turn 3 today and looking back, I have so much stuff that was not necessary. My goodness, the clothes. We have decided we will have no more children so I will be starting to part with their items. I probably needed a third of what I had. It adds up quickly and you really just don't need as much as the baby stores make you think you need. Good luck!