Quote: Do you think a cotton hankie is better than the "proper" lens cleaning cloths?
Honestly, yes.
Quote: What cleaning fluid is best to use?
Haven't noticed any difference but do not try tape head cleaner, which contains a glycerol-based detergent which will cause smearing.
Quote: Some of the fluid I've used has left quite bad smearing behind.
Presumably because the lens was greasy to start with. This is why I suggest cotton, if scrupulously clean it will absorb grease quite well. And the lens pen will finish it.