NTC Resistance considerations
Typically the usable range will be the same regardless of the resistance at 25°C. The datasheet will tell you what range it is rated for and the accuracy at various temperatures (typically it will be most accurate at 25°C and less accurate the further you are from 25°C). 

The dynamic range is an issue with thermistors. At high temperatures the resistance will be much lower than at 25°C so it may be more convenient (or require less expensive circuitry) to use a higher resistance thermistor, and if you have long wires to the thermistor their resistance may start to have an effect on the measurement. 

Another factor is self-heating. You can calculate that from the power dissipated in the thermistor. Note that thermistor data sheets typically will show self-heating (and response times) in very favorable conditions such as water moving at 1m/s. In still air the performance will be much worse. 

Typically NTC sensors change around 4% per degree C, so a 1% resistor is called for if you are looking for 1-2°C accuracy. Also an accurate thermistor- not only the tolerance at 25°C but the tolerance on \$\beta\$.