Congrats on getting it up and running! It looks like you only have a half wave rectifier circuit going there, and either low capacitance or low resistance.
One rule of thumb for input filters is that your RC Time Constant should be around 10 times your input period. For 60Hz, we would divide 83(full wave) or 167(half wave) mS by the load resistance, to get the desired filter C in Farads. You could experiment with different calculated values and observe your ripple amplitude. Can you imagine what the output of your LM317 or LM350 circuit would look like with this as your input???
Joe