Choosing the correct flyback diode
The diode will have to withstand the full operating voltage of the relay (since it will be anti-parallel to it) and also the full operating current since this current will flow through the diode when the relay turns off. This is because the current through an inductor can't change instantaneously (dI/dt is proportional to the voltage across the inductor), which means that once the controlling transistor switches off, the full relay current has to go somewhere.
If you want the relay to turn off faster, you'll have to increase the voltage across it during turn-off, which you can do with an additional Zener diode in series with the flyback diode. That way the current through the relay's coil decays faster. Of course this means that the driver (i.e. transistor) driving the relay has to withstand this higher voltage.
The power rating of the diode most likely won't matter as you're not going to switch the relay at a high enough frequency to dissipate substantial power in the diode. If you want to calculate it anyway, the formula for the diode's power dissipation is P = 1/2 I²Lf, where I is the relay current, L the relay's inductance, and f the frequency at which you switch the relay on and off.