Honestly, we are marketed too much as a new Mum. You don't need much. You can always buy things as you feel you need them. Less is more when your baby comes. As long as they are fed, warm and close to you, they don't need much more.
My boys still use hooded towels at 2 & 3.5 years
Yoofoss 2-Pack Hooded Baby Towels 32x32
I used one of these until my babies were 6 months old. It's also great for Dad when you need a break.
Boba Baby Wrap Carrier - Newborn to Toddler
When bub gets too heavy for a wrap carrier
Infantino Flip Advanced 4-in-1 Baby Carrier Gray
I didn't actually have one of these (it would have been helpful) but I gifted one to my cousin who loved it
Parker Baby Diaper Caddy - White, Regular
Rinse & repeat
Gerber Baby Boys 4 Pack Sleep 'N Play Footie
For the girls
Onesies Baby-Girls 4-Pack Sleep 'N Play
If you're in a hot climate but even then, I preferred full onesies.
Kiddiezoom Newborn Unisex Cotton Bodysuits 5-Pack
If you want get your shopping over and done with
Spasilk Baby 23 Piece Layette Set 0-6 Months
The best thing for any nappy rash or scratches (and cracked nipples).
NOW Foods Pure Lanolin Skin Protectant 7oz
I needed a few of these with my first but not my second
Muslin Swaddle Blankets 3 Pack, 38x40, Bright
No essential but it can be nice brush their hair
MYZI Baby Hair Brush & Comb Set Newborn
We even used this on the floor instead of a change table
Kopi Baby Portable Diaper Changing Pad Travel
Clean, rash free nappies are worth the investment
ECO BOOM Bamboo Viscose Diapers Size 0, 34ct
A great water bottle in your caddy is a must postpardum