A first approximation for the choke size is that it will be at least as big as the power transformer, and will likely also be a custom wound component, as it needs to be wound with a nice air gap in the core ( often implemented as an angled slot in the middle leg and thus made not from the common EI laminates but from a less common EE laminate with the centre legs cropped slightly) and also has to have a low DC resistance, thus is wound with a thicker wire.
You can do a choke filter with a SMPS and have it come out as small as the regular transformer, and gain a good amount of efficiency from lower diode losses in the rectifier on the output, but on a 50/60Hz transformer you will be always better off ( aside from one application) with a bigger transformer, beefier diodes and living with the ripple. It does reduce the diode peak current, and increases conduction angle, and in some designs is actually an energy store that provides power to the load as well during half the cycle.
The only time that it makes sense is in high voltage supplies, where you are limited in component values either by the diode ratings, or the ripple current ratings on the capacitors and thus have to use lower value capacitors than you want, and then use a LC smoothing choke to reduce the noise ( you can use RC smoothing, but this only is useful at very low power as the resistor is a hot component) on your high voltage supply. This is common in valve equipment, especially high power amplifiers, that need a low noise ( but not terribly well regulated) power rail for low noise operation, and where the complexity of having a choke capable of withstanding the high voltage from the coil to the core is easier than trying to fit a bathtub sized capacitor in the housing along with the inrush limiting for turning it on. You can get a lower value capacitor ( 22uF or 47uF 630VDC) and have a lower turn on inrush, along with much lower diode peak currents.