What a liner does
Three things. It contains combustion products so they cannot reach the masonry or the framing around it. It protects the masonry from acidic and corrosive by-products, which matters enormously with gas and oil appliances. And it provides a passage sized correctly for the appliance, which is what allows the appliance to draft as designed. The third is the one people underestimate, and it is frequently the one that turns a disappointing stove into a good one.
What it does not fix
A liner will not cure a draft problem caused by house pressure, by a blocked cap, by a chimney too short for its roof, or by a fireplace opening out of proportion with its flue. It will not repair a failing crown, spalling brick or bad flashing, and installing one into a chimney with those problems means doing the masonry later with the liner in place. Anyone proposing a liner without having established the cause of your actual complaint is selling instead of diagnosing.
Where insulation changes the answer
On an exterior chimney in this climate, a cold stack on an outside wall, which describes a great many Vermont houses, an insulated liner does considerably more than a bare one. It keeps flue gases warm enough to establish and hold draft, which improves how the appliance runs, and warmer gases deposit less, which reduces creosote. Also sometimes what allows the required clearance to combustibles to be met where the chimney passes through framing.
How to tell whether you are in situation three
You would need a camera scan showing sound tile with intact joints for the full flue length, and an appliance whose outlet matches the flue size. Both of those are findings, not assumptions. Both come from a Level 2 inspection. If nobody has scanned your flue, you do not yet know which situation you are in, and that, instead of a price, is the useful next step.