On the question of insulation, I recommend it if there is room in the chimney for the liner + insulation. Insulation keeps the gas hot as it exits the house which is a good thing. Hotter gasses rise faster, therefore the insulation will improve drafting. The gasses staying hot also reduces the build up of deposits from gas condensation. Maybe this is less an issue with natural gas exhaust, but with a wood burning stove you will get more rapid creosote build-up on the liner and therefore must clean it more often if you skip on insulation. You don't want a chimney fire.

Edit: I should make it clear that I am not a professional, just a DIY guy with a degree in physics. My opinions are worth what they cost you. :)