Hi there, I am new at this too, not having actually yet used any that I have bought for our soon-to-be-arrival.
I'm sure someone with expertise will be along any moment to tell you all the right things but I'm not sure you can get a pocket with natural lining as it is usually the natural fabrics which are used as the absorbent bit as they do a good job of it and the synthetic fabrics are like a stay-dry kind of liner against the skin.
Hope you get what I mean... lol my brain dont work like it used to!!!!