Full wave rectifier with inductor filter
If I understand right, Your question whether you should require little to no ripple in the output voltage from your power supply. 

Well, all power supplies in the world have some ripple and typically circuits that eventually are the power consumers will tolerate some ripple. In general you would not want your power supply to provide lesser ripple then what your consumer desires because that would add drastically to the cost and complexity of your power supply. As an example you have used 2.2mF capacitor and 100mH inductors. A 2.2mF capacitor of 50V or above would be a gigantic one. A 200mH 2Ampere inductor wouldn't be a small component either.

In your specific case the answer depends on the type of linear regulator you are planning to use. Lets say you want to use a 5V regulator like a 7805 then having fair ripple like around 8 to 10V could easily be tolerated. Typically linear regulators have internal or external feedback loops to compensate for output voltage changes against a reference but you wouldn't have to worry about that considering that the ripple frequency is going to be around 100Hz(the rectifier doubles the frequency as the waveform is just one sided). The max allowed ripple will depend on the final regulated voltage that you desire. So your linear regulator's datasheet will dictate what is the minimum input voltage it can have and still provide a stable constant output.

Now all being said, in short, if you are eventually going yo use a low voltage linear regulator, it seems you dont need such large inductor or capacitors. 

If you have further interest in low ripple power converters and that without using very large components, you should study high frequency/switch mode converters. Typically switched converters would feature an IC/microcontroller that would switch a device(mosfet) using a high frequency PWM to achieve target output voltage and that too without a very large size of components. 

FYI thats how phone chargers that used to be really bulky suddenly got so compact around 2 decades ago because all of them now use SMPS. 

Best of luck learning.