Selecting bias resistor for thermistor
With a simple resistive divider, you won't be able to stretch the range of output voltages to cover the full range of the ADC input, but you'll get the best overall resolution by setting your bias resistor to the geometric mean of the minimum and maximum resistance values of your sensor (for the temperature range of interest).

For your specific setup, that would be \$ \sqrt{4K * 115K} = 21.447K \$

You could select a 21.5K 1% resistor or a 22K 5% resistor. The voltages you get will run from 15.7% to 84.3% of the ADC input range.

To get output voltages that cover the full range of the ADC, you'll need an active (e.g., op-amp) circuit that has gain and offset capability.