Does using voltage regulator in power supply further reduces the rippling?
Adding a linear regulator will significantly reduce the ripple, but it has its downsides.

1) The regulator has a minimum "dropout" voltage, in this case about 1-2V depending on current.  To account for this, your first stage needs to have an output voltage greater than 12V by at least the minimum dropout voltage - so, maybe 14V.

This means you're dissipating some power (V_dropout * I_load) in the linear regulator.  In addition to power loss, you may have to pay attention to heat sinking it appropriately.

2) Depending on the ripple before the regulator, you may have to increase that "drop out" voltage even further, because you have to do the dropout calculation based on the minimum value of the ripple waveform (not the average "DC" value).

The advantage of the linear regulator is that the final waveform will be perfectly clean - the final ripple will be plenty low enough for almost any load.

So, what's the right approach?  Depends on your load.  If you're powering, say, a heater, the ripple probably doesn't matter.  If you're powering a circuit with a secondary power conversion (IE, it takes your 12V and converts it to 5V), you're probably ok with high ripple, depending on the quality of that 12V to 5V converter.  If you're directly powering something sensitive (say, an amplifier or other analog circuitry), you probably want to use the regulator.