There are heaps of great natural products available for babies. The most affordable range available in New Zealand (that I know of) is Ecostore. The range consists of:
Baby Shampoo 200ml $10.95
Baby Body Wash 200ml $9.95
Baby Sleepytime Bath 200ml $10.95
Baby Soap 80g $3.65
Baby Nappy Balm 60ml $11.95
Baby Moisturiser 125ml $13.95
Baby Massage Oil 200ml $13.95
These are the prices according to their websites, but they are quite a bit cheaper in supermarkets. I used to use the Baby Soap and Baby Moisturiser (on myself), and I like to use the Nappy Balm for moisturising my cuticles, dry bits between my fingers, rough heels, etc. I don't have a baby myself, so I can't tell you how well it works at preventing nappy rash!
Another affordable New-Zealand made range is Made 4 Baby. Their products are available in Fragrance Free, or the yummy-smelling Organic Citrus. They have some gift packs, which would be great to give to new parents. Check out their list of stockists on their website.
GAIA Natural Baby has a great gift pack called Baby Starter Kit. For $34.99 you get Baby Bath & Body Wash, Baby Shampoo, Baby Moisturiser, Skin Soothing Lotion, and Baby Massage Oil, each in a 50ml bottle. I have seen the GAIA baby products at Babycity, and at a pharmacy (can't remember which one, sorry).
Living Nature's 'Kekebaby and 'Kekemama range also has a couple of gift packs. I blogged about them previously, check it out here. They have some products for mums, as do several other baby ranges, like Weleda's baby range, which has a Nipple Care Cream, $11.
I spotted a very cute range of baby body care products in a gift shop recently - Peter Rabbit Baby Care! The packaging has pictures of Peter Rabbit on it, the ingredients are all natural, and some are organic. There are six products, all $26.90 each. Bod for Bubs also has a nice range of baby products.
For babies six months and over, a good sunblock is UV Natural Sunscreen Baby SPF30, $18.50 for 50g, and $35.90 for 150g.