Boogie wipes, humidifier, bulb syringe (or any other nasal aspirator), mittens for when baby is tiny, nail files (I never felt safe clipping my daughter's nails the first two months), teething toys (especially the refrigerator gel kinds), boppy pillow For feeds.
For you: breast pads, breast gel inserts (these no matter what feeding method you use), breast pump (if you're nursing).