You could probably run the fan directly from the bridge rectifier. The voltage may be quite a bit bigger than 24 V, and will have loads of ripple, but fans are tolerant of poor power supplies.
A capacitor of about 2200 uF or more would reduce the ripple a lot. The voltage will also go up.
You could use a regulator to hold the voltage at 24 V if you want. You could also adjust it to alter the fan speed.
It depends on how much current you want as to what sort of regulator is appropriate for the 5V.
A zener regulator is simplest, but is hardly any worse than a linear regulator if the current at 5V is fixed. The current taken by a zener regulator is the same whatever the load.
A linear regulator is still quite simple, and the input current is about the same as the output current.
A buck regulator is much more efficient at large loads, but a lot more complicated.