Define "good gas sensor", which in this case means defining the range of measurable values and required accuracy of measurements.
$100 per sensor is very unrealistic. For example, methane is a trace gas in the atmosphere, so you would be looking at industrial quality leak detectors for use in harsh environments. Methane Gas Sensor | Best Gas Leak Detection | NevadaNano
Currently, methane concentration (by mole fraction) in the upper atmosphere is slightly less than 2 ppm.
To have any chance of winning, you really need to do some very basic research. The judges will instantly recognize and reject those proposals lacking fundamental understanding of the problem.
We would need the sensors calibrated if our proposal gets accepted. However, we first want to pass the selection phase, we can worry about calibration later.
Then make a friend with the head of the chemistry department at your nearest university and ask for their help. They will regularly calibrate gas sensors.