A good thermometer

Baby Tylenol (wait for your pediatrician to tell you how much -- but there are shortages, so buy one just in case)

A can of formula, bottles, and pacifiers -- better to have them and not need them -- then need them and not have them. Milk doesn't always come in right away. Baby still needs to eat

Hats

Jammies that cover their hands -- babies have ridiculously sharp nails and they scratch themselves constantly

Wipes

Newborn and stage 1 diapers -- they outgrow the newborn ones quickly. Be careful not to buy a ton of diapers, babies can be allergic to certain brands. Wait and make sure that the brand you like, your baby isn't allergic to

Zippered onesie pajamas --- don't buy anything with snaps or buttons

Onesies

A good unisex diaper bag

Highchair

A good zippered cold weather sack

A cover for the car seat to protect from the cold

A bouncer/bassinet/swing all in one

We had an expensive fancy stroller -- it was big, took up the trunk, and hard to deal with. We ended up buying umbrella strollers for $20

People will flood you with toys, books, blankets, and stuffed animals -- skip those for now

What I would skip is the baby bathtubs -- I would hand the baby to my husband in the shower or he would hand the baby to me for a quick bath --- those baby tubs are very awkward to store