How about this MOSFET, it has a nice low on resistance:
https://uk.rs-online.com/web/p/mosfets/7840290/
There are a few things to note about that mosfet. Firstly, it has a gate capacitance of several nF for a certain set of conditions, that may be less onerous than the ones you'll face. Secondly, it is a logic level device which means that it may be slower to turn off if the gate is just pulled to 0V.
The higher the gate capacitance, the higher the gate current required to switch the device in a given time. I have seen gate drivers capable of driving the gate of mosfets with a higher current than will be passed by the mosfet itself! A driver capable of several amps is not unusual. Unless you actually require a logic level device and a low Rds(on), compromising on these can allow you to select a device that will be capable of faster switching, or switch much faster without needing exotic gate drivers.
In your case, even an Rds(on) of 1Ω would result in only 16W of dissipation, and you have sufficient voltage from your power supply to be able to cover the 4V dropped by the device. I'm not suggesting that you should be looking for 1Ω, just that 0.015Ω is clearly not a requirement. Maybe devices up to a couple of hundred milliohms should not be excluded.
Using a gate driver like the one I suggested allows you to use a device with a higher Vgs(th). This means the gate driver does not have to pull the gate as close to zero volts before it switches off. Thus, pulling to 0V may be sufficient, rather than having to use a negative rail. This is less of a consideration in your case, however devices with low threshold voltages also frequently have higher gate capacitances, feeding into the problem mentioned above. Because the gate driver can swing the voltage through a larger range than the output of your microcontroller, the need for a logic level device is removed.
To increase the speed of the driver even more, a schottky diode can be placed with the anode to the base of the first transistor and the cathode to it's collector. This prevents the transistor from saturating. Whilst this will also prevent the gate driver from pulling so close to 0V it will significantly increase the switching speed.
In general bjt's do switch a lot faster than mosfets (to answer another of your questions). Mosfets have an advantage in lower ON resistance, typically resulting in lower voltage losses (and therefore lower dissipation with consequent reductions in the size of heatsinks).
