Most products designed for curly hair are sulphate-free (and your hair doesn't have to be curly to use them, obviously!).
I use Only Curls, but the Noughty range is good, too - sulphate / paraben / silicone-free, cruelty-free, vegan, UK-made, recyclable packaging and pretty widely available - Boots and Waitrose stock it. Not 'cheap' cheap, but considerably more affordable than most.