I would avoid getting cocky if you are asking for assistance around here.

As an electronic engineer with over 40 years experience I can tell you I have NEVER heard anyone refer to a capacitor as having an anode/cathode - I don't care what Wikipedia says - they are WRONG!

You will need a cap with AT THE LOWEST, 63V rating for your application. You should also refer to the application data for your chosen regulator. They require a small cap on the input and output legs as close as practicable to the part to prevent oscillation.

Build the circuit WITHOUT the regulator attached and measure the voltage at what would be the input to the regulator. If it is higher than about 45VDC (very possible) your regulator won't like it - again, refer to the data sheet for exact voltages.

Good practice would also dictate adding a fuse in one of the AC leads at the very least.

See the post 2 above yours....

"You should also refer to the application data for your chosen regulator. They require a small cap on the input and output legs as close as practicable to the part to prevent oscillation."

No, not at all!

But you might just have realised that to be knowledgeable in electronics requires YEARS of tuition, study, working in the field and stuffing up many things!

You can't possibly understand the myriad of things you need to know to design even a simple circuit without the above.