Putting a large-valued cap across 50Hz or 50Hz AC will cause it to draw LARGE amounts of completely wasted current (==> power). The larger the cap is the larger the waste will be. You really want a SMALL, low-inductance, low-ESR, high frequency, non-polarized cap to filter out any HIGH FREQUENCY noise.

The transformer’s winding’s polarities are POINTLESS! We’re dealing with A/C.

The min size of the output cap and the bleeder resistor are completely dependent on the max current drawn from the supply *for a desired minimum amount of voltage ripple*. The values are proportional to the max output current drawn by a particular application.

Using 3 transformers instead of just 1 will drastically reduce the max power output of the supply. Assuming 85% transformer coupling efficiencies, the max output of 3 # 50 volt-amp transformers will be only 50VA x 85% x 85% = 36 volt-amps. (The effic. drop from the first xfrmr has been accounted for.)