Estimate data transmission rate on a given frequency using FM
Frequency and the use of FM actually have little to do with it. Although at 100 km range, the propagation characteristics of different frequencies will come into play.

The key parameters are SNR (signal-to-noise ratio) and bandwidth (BW).

The Shannon-Hartley equation for channel capacity (C) tells us:

$$C = \text{BW}(1 + \log_2 \text{SNR})$$

For maximum robustness against fading (poor SNR), it is normal to pick a modulation scheme that requires about 1 Hz per bits/second. But high-bandwidth applications such as digital TV use more complex schemes that might transmit as much as 6 bps/Hz.

However, for the distance you're talking about, you're going to need power levels that will require a license to use. This means that you're going to have to figure out what kind of license you'll need in your country, and this will dictate things like the frequencies and bandwidth available to you.

If this is for non-commercial purposes, it's possible that an amateur radio license would be appropriate.