Choosing the correct thermistor
The most suitable thermistors for temperature measurement are NTC types. The sensitivity is similar for most types (Beta in the range of 4000, give or take). If your range is 5°C +/- 5°C you might have an output of 2.5V +/-0.3V. If you want more like 0-5V you'll have to offset and amplify it. 

Physical characteristics have to match the requirements- leaded, SMT, waterproof etc. 

Other than that,  the main thing is to pick an accuracy that is good enough and a resistance that is high enough that self-heating does not cause too much error, and not so high that whatever is reading it has problems (for example, an ADC might specify no more than 2.5K source impedance*. If the latter is a problem then a buffer amplifier can be added. 

* the maximum source impedance is 1/(1/R + 1/Rtm) where Rtm is the resistance at the minimum temperature (maximum resistance).