The short version
Newborn skin needs less, not more: warm water, a fragrance-free wash two or three times a week, and plain coconut oil for the massage. Besan and haldi dry the skin, and mustard oil has been linked to irritation.
What happened
On day ten, my mother wanted besan and haldi. My mother-in-law wanted a mustard-oil massage before the bath. The paediatrician wanted neither and said "warm water and a mild wash, twice a week." I was holding a baby and three strong opinions.
What we did, in the end, was all of it in moderation, because the massage is about more than skin. The daily oil massage before the bath, with a plain coconut oil rather than mustard, became our best twenty minutes of the day: he relaxed, I relaxed, my mother-in-law got to do the thing her mother did. Only when a dermatologist friend mentioned that some traditional oils can irritate newborn skin did we settle firmly on coconut.
The besan-and-haldi paste I let go after one try. It left his skin dry and the haldi stained the muslins orange for a month. The dermatologist's view is that newborn skin needs less, not more: water, a fragrance-free wash two or three times a week, pat dry, done. Soap every day strips the barrier.
On washes, the same rule as creams: read the back. Most 'natural' baby washes in India are coconut- or lavender-scented, which is fragrance by another name. We found one that genuinely listed none, and used it twice a week. The rest of the week, warm water.
Three years on: oil, warm water, two washes a week, and the grandmothers get to do the massage on weekends. Everybody won something.
The American Academy of Dermatology recommends mild, fragrance-free baby soap and shampoo, and fragrance-free detergent for baby clothes. Daily emollient from birth has not been shown to prevent eczema (BEEP trial, 1,394 infants), so oil and lotion are for comfort and dryness, not prevention.
AAD, How to care for your baby's skin, hair and nails. Source · BEEP trial summary. SourceThe verdicts
Plain cold-pressed coconut oil (kitchen grade, no fragrance)
For the massage. Cheap, fragrance-free, and what the grandmothers agreed on once mustard was off the table.
A fragrance-free baby wash (check the list, not the front)
Used twice a week. Brand matters less than the absence of parfum. I've listed what I could verify below.
Cubworthy, with a catch
Mamaearth or Baby Forest body wash
Popular and gentle, but the listings I checked are coconut-scented or don't state fragrance-free. Fine if your baby has no reactions; not what I'd choose for sensitive skin.
Besan and haldi paste
Tradition says yes, his skin said no. Drying, staining, and no evidence it does anything a wash doesn't.
Product details are as we used them; the version on sale now may differ. Check the exact model and the manufacturer's instructions.