A lot of us fully rinse out our thicker conditioner, then apply a leave in conditioner (even if we use our rinse out as a leave in). For me, I feel I have better control over the amount left in my hair when I completely rinse my RO out of my hair, then add my leave in. Some do prefer the "partially rinse the thicker conditioner and go" method. You'll have to experiment to see what works better for you.
On the sulfate shampoo, be sure whichever one you use is silicone free, otherwise you'll leave silicones in your hair which hinder your hair from optimal moisture absorption. Suave Naturals shampoos are cheap and are all silicone free if your current shampoo is not.