It is reasonable to start with a frequency of 20 kHz. This is above the range of human hearing, so it is less likely to make distracting noise.
The Henry value, together with the resistance in the first half of the cycle,
will create a time constant (L/R). You need to choose values so that amperage can reach maximum in the amount of 'On' time in the first half of the cycle.
A Henry value of 1mH is commonly available, and not too expensive. Maybe 500 uH. The value is flexible, since your controller will change frequency and duty cycle, to reach optimum performance.
Notice that the more current a coil carries, the larger it will be and more expensive it will be. A smaller Henry value becomes attractive in those cases.