Watch the no sulfates shampoos from teh health food stores, I know for sure Jason's has a cone in it. It makes my hair very tangly.

Activate makes a very good shampoo no cones and no harsh cleansers and it's pretty reasonable. I like creme of nature, it's cheap, found at walmart and not drying although some do find it is too conditioning. For the price it's worth a try though if you like No poo.

If you want a mild shampoo Elucence makes one, moisture balancing shampoo. You can buy it pretty cheap by the liter and a little goes a long

ETA: oh and yes your hair could like sulfates. Maybe they take off what weighs your hair down and lets the curls spring back up.
Low porosity, medium texture.

If it smells good put it in your hair, if it tastes good spit it out!