Usually this is simply chosen so that for the given primary current you get the required voltage.
Say you need 1V at 1A with your transformer. The secondary current is going to be 0.1A when the primary current is 1A. So R=1V/0.1A=10 ohm.
There are other things to consider, but you are not designing the current transformer, you are just using it. So that's pretty much it.
A single rectifier will do. Generally, the 1N4148 is a good choice. Just make sure you do not exceed the peak current, or choose a different diode. A fast diode is always a better choice.
I hope that you know that you may have to factor in the diode drop to get required accuracy.
1N4148 has upto max of 1V.
Maybe some further reading on precision rectifiers,could be useful.