As jiripolivka said, both the diode and capacitor will depend on your current. If your current draw is upto 1 amp in 110v DC, any 1n4004 or higher diode can be used. If your current draw is higher than 1 amp, you need to choose a higher current rating diode, such as 10A10.
A filter capacitor is needed to minimize the ripple voltage. It should be a electrolytic one. Use this formula to find a suitable capacitor.
dU= I/2fC
where dU is peak to peak ripple,
I is load current,
f is operating frequency and
C is capacitor volume in Farad
.
In this way you can choose ripple amplitude and from equation estimate
capacitor volume. For example if you have 1A current and capacitor
4700uF ripple will be
dU= 1/(2*50*0.0047)= 2.12V.
As you can see, capacitor value depends upon the current flow, not the operating voltage. But while choosing a cap, use a voltage rating of more than 250v.