smoothing capacitor for power supply
No filter cap at all will be necessary.  But for reversing, you are going to want to put a time delay between forward and reverse, preferably use something like a three pole switch, and give the motor some time to spin down before switching its direction.
And you might want to forget just feeding the bridge rectifier directly, and look at an SCR drive controller or even heavy duty SCR light dimmer to feed it.  That will give you variable speed.  If using a drive controller, you won't need the rectifier.  If using just a heavy duty light dimmer, you will.