What should I be using to clean their hair?

My boys have curly hair and I have been trying to find a tear-free type shampoo for them (2&3 years old) that is budget friendly. Would using a chemical free shampoo be the same as a curly hair formula? Most things I have found are expensive or for mixed hair and theirs is not. I haven't done much curl care for them yet other than not drying w/o diffuser and no brushing. I will sometimes use products on their hair when it needs to look nice (family photos etc.) but am wanting to not do too much damage to their hair. And what are the curl types and what do they mean? 

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