Material and grade: match the alloy to the fuel
Stainless liners come in different alloys, and the right one depends on what will be burned. Wood, gas, oil and coal produce different combustion by-products with different corrosive behaviour. A liner in an alloy that does not suit the fuel is not a long-term component, and the difference is invisible from the room. Ask which grade is specified and why. Write the answer down.
Diameter: sized to the appliance, not to the chimney
The appliance outlet defines the correct diameter. Fitting a larger liner because the chimney has room is the classic error: draft depends on keeping gases warm and moving, and an oversized passage lets them cool and slow. That means weak draft, smoke coming back and creosote building far faster than it should.
Insulation: often the thing that makes it work
Insulating the liner keeps flue gases hot enough to establish and hold draft, which matters most on exterior chimneys and in cold climates. It also reduces creosote for the same reason, and it can be what allows a chimney running through framing to meet its required clearance. On a cold Vermont wall it is frequently the difference between an appliance that works and one that does not.
Termination and what happens to the old tile
The liner needs a proper top plate, cap and termination, and where broken tile leaves too little room for the correct diameter, that tile is broken out to make space. Both belong in the scope explicitly. A quote silent on the existing tile is a quote that may be planning to fit an undersized liner instead. Ask about it directly.