If you want to use a natural hand wash, there are plenty to choose from. The most affordable one I know of is Viola Organics Liquid Hand Soap, $6.50 for 250ml, and $9.95 for a 500ml refill bottle. It's available in Lavender, Summer Fresh, and Unscented Mild/Baby. I have tried it in the Unscented, and I like it, though the texture of it is very thin, about the consistency of water. It takes a bit of getting used to, but it foams up really well.
I also like Sukin Cleansing Hand Wash, $12 for 250ml, and $27 for a 1 litre refill bottle. This is a lot thicker than the Viola Organics hand wash.
Some other options:
$15 and under: Natural Instinct Hand Wash 250ml $12, Aveda Rosemary Mint Hand and Body Wash 50ml $13, Living Nature Purifying Hand Wash 250ml $14, A'kin Hand Wash 240ml $14.90, available in Eucalyptus & Tea Tree, and Lemon Myrtle
$20 and under: Blue Earth Flowing Soap 300ml $15.50, available in Oranges & Lemons, and Lavender & Rosemary, Tebe Hand Liquid Soap 280ml $15.80
$25 and under: Duchy Originals Liquid Soap 250ml $24.90, available in Rose & Mandarin, Bergamot & Lime, and Lavender
$30 and under: Natural Instinct Hand Wash Refill 1 litre $27
$35 and under: Emma Green Pohutakawa & Kanuka Hand Wash 500ml $33
$40 and under: Aveda Rosemary Mint Hand and Body Wash 250ml $40