A transformer, not rectified. A Scalextric Sport works. Or break up any other and start out before the rectifier.
Four rectifier diodes, not a rectifier bridge.
Car to drive:
One rectifier diode.
A rectifier bridge and a nine volt voltage regulator.
Ok, you can only drive two cars. But shadow cars start and stop as the driven cars do. So no pile up's if both drivers stop.
One AC "pole" (let's call it Red) is separated by one diode sending minus to the left rail. And a plus giving diode goes to the controller and then also to the left rail.
Another AC "pole" (let's call it Green) is separated by one diode sending minus to the right rail. And a plus giving diode goes to the other controller and then to the right rail.
Even numbered cars have a diode from the left side braid to the right side of the motor and a simple wire from the right braid to the left side of the motor.
Odd numbered cars have a diode from the right side braid to the right side of the motor and a simple wire from the left braid to the the left side of the motor.
Shadow cars have a rectifier bridge from the braids and then a 9V voltage regulator to the motor.
Ok, then you'll need to power the points from their own power source. And install MCR to control them.
Apart from these steps it's a €1 two car digital system. Enjoy!