Which one would be the preposition of choice when discussing the number of times something happened? Examples:
I saw her for the third time. She is visiting me for the first time.
You should use por in most of the cases.
La he visto por tercera vez.
Me visita por primera vez.
I cannot think of any case where you would use para for a number of times type of sentence.
Anytime you refer to time at all, you will use por
.
If you were to say
Escribí una caricatura para tres minutos
It would suggest that you drew a cartoon FOR 3 minutes, not as in time, but rather, for, as in a gift. In other words you would be drawing a cartoon as a favor to 3 Minutes, as if it were a person/business/entity/etcetera... named "3 Minutes"