Here is a list of items I found helpful during first few weeks!

Jaz • Mom to two beautiful daughters and another on the way!! Happily married for 9.5 yrs.
As a FTM - I went all out buying anything and everything. And then when the baby was born - I realized a few things were truly essential.  Every baby is different - but this worked for me:
Swaddles (double swaddle) - the Aden and Anais ones are wonderful - they are large and super soft (great for warm weather
-the miracle swaddled are nice too because you can't swaddle their legs in place because it can cause hip  dysplasia.  
Glowy the Seahorse- this is a fisher price toy that lights up and hums songs for 5-minutes.  This helped my baby sleep at night as I rock her in the rocking chair. 
Baby carrier
-I have a ring sling and a lillebaby.  The ring sling works wonderful for how tiny she was (5lbs-11oz).  She sleeps in it as I do chores and I was even able to wear her to the movies w/o any issues (judge if you want)
- The lillebaby is awesome too but I felt more comfortable w the ring sling since she was so tiny.  I know I will use this one a lot though once she is bigger and has better head control.
Infant car seat and stroller - trust me - although I love baby wearing - this has been a lifesaver!!!
Diapers and creams and wipes
- you will go through a lot of these - so buy them in bulk.  I didn't buy too many newborn size bc I was not sure what size my baby would be - so I did have to buy some more premie and newborns - but sizes 1-3-I have in bulk.  
Diaper genie
-my husband and I went back and forth w this one.  But we were gifted two - a small one and a regular size one - and it has worked wonders!!!  Trust me!
Swing
-my baby girl slept in this for the first 2.5 weeks!! And she still takes naps there occasionally 
Nipple pads (to prevent leaking) - I bought the bamboobies (reusable) and I love them!! 
Nursing bras - trust me!  If you are breastfeeding - you need a good collection (I love the ones from motherhood maternity - the pullover sports bras and the seamless)
Nursing tops - if you thought nice maternity clothes were hard to find - nursing tops are even harder-so start searching early! 
Boppy - we brought ours to the hospital and it was a lifesaver.  I still use it occasionally.  It's def a nice to have! 
Good luck ladies!  If you have other items that were necessary that first month - please comment!!