Does any shampoo without harmful ingredients work or does it need to be specifically related to that kind of hair?

So for example, I just placed an order for a shampoo called 'tgin' which is: (Moisture rich, Sulfate free, paraben free, Lanolin free, Petroleum free, Mineral oil free, and no artificial colors).

Is that good enough? It is just a regular shampoo. So I wanted to know if there's any problems with this. (For remy hair)

Or do I need only specific hair products for my hair system?

It costs $16 for 13fl oz. so I wanted help before just wasting income on products I don't need.