First PSU - need help with capacitor size
Define your maximum ripple voltage: ΔV (also called dV, V ripple). Look at image below and I guess you should figure it out.
Use this formula to determine minimum capacitor capacity.

\$C = \frac{I}{Vpp * 2f}\$

where: C is capacitor capacity in Farads (1F = 1000000uF), I - current, Vpp (or delta V) - voltage change on capacitor when it is being discharged, f - frequency before bridge

This method can be found in wikipedia article about ripple, just in diffrent form (formula on wikipedia calculates ripple at given capacitor).




Image source: wikipedia article mentioned above + me


Use capacitor with voltage rating at least a bit higher than your transformer amplitude, not RMS voltage. Amplitude for sinuoid after full bridge is:

\$Vpp = Vrms * \sqrt{2}\$


In your case it will be about 17,8V, so you cant use 16V capacitor.

Also notice, that transformer open circuit (no load) voltage may be much higher than nominal.