What type of chimney is best
There are advantages and limitations to each kind: Masonry chimneys incorporate traditional beauty that many homeowners want. Factory-built chimneys offer a non-masonry option that often proves easier to install, at a lower price. Some types of chimneys are designed only for appliances that burn certain fuels.
Determining the best type of chimney for you requires a complete picture of the specific appliances (fireplaces, wood stoves, furnaces, etc.) that the chimney must serve, and the specific venting requirements for those appliances.
For example, factory-built fireplaces often require specific types of factory-built chimneys, while most wood stoves can be connected to either a masonry chimney or certain types of factory-built chimneys.
If you plan to have a new chimney installed, first find out what type of chimney you need for your appliance. Check the owner's manual for wood stoves or factory-built fireplaces. Chimney requirements should be spelled out pretty clearly.
If you plan to install a new (or used) appliance into an existing chimney, you need to do the same thing. It could be disastrous, for example, to connect a wood stove into a chimney that is designed only for a certain type of fireplace. Don't assume that you have the right type of chimney. Find out for certain.