Before choosing what type of sensor you really need to know what the maximum temperature might be at the point you are measuring.
If its less than 200C the most accurate would be a PRT (Platinum Resistance Thermometer). A 3 or 4 wire PRT100 can be wired with microscopically thin wire and as long as all wires are the same length remains accurate.
Over 200C a thermocouple is better and more likely to be robust.
The high temperature capability of a thermistor will depend on how its packaged so its range is similar to a PRT, but its a much lower cost. Thermistors are very non-linear compared to PRTs and thermocouples and you might need to use some maths or a look up table to display accurate values.
Solid state sensor will be encapsulated in plastic so that limits the upper temperature but if you use an intelligent sensor it will give a ready calibrated digital output without any interfacing or analogue circuitry.
PRT and thermocouple signals need analogue circuitry but in general are the most accurate, however they will end up more expensive than other sensors.
I no longer have a wood burning stove but I have a feeling that the flue exit temperature will be in hundreds of degrees and a thermocouple may be the best choice.
Ian P