You do not need anything but water. Occasionally any soap will do. Breastmilk has a lot of mousturising and cleaning properties.

I remember our midwife saying only use products from 4-6 weeks old and then start with an non-perfumed product and a tiny amount on the hair only and we only washed bub every 2 days or so for the first few months as this was suggested to us by the midwife as it’s better and less drying for their skin

We used Avo baby it’s great and really gentle (I read up on the ingredients) you can get it in Priceline or online here – still use it on my bub and he is almost 3 now
https://avobaby.com.au/products/balancing-hair-body-wash

Also, I know you didn’t ask about cradle cap but if there is any cradle cap a mothercraft nurse suggested to us a cotton ball with coconut oil massaged into the scalp after bath time at night and this tip was invaluable it really helped so much!