Both
la radio and
el radio exist, but are different words. And you certainly want to call the Pope
el papa, not the Potato (
la papa).
In my opinion, you should learn the article along with the word. In some cases, it's best to learn the plural article instead of the singular (
el agua, but
las aguas (
agua is feminine, but a masculine singular article is used for euphony's sake)). Others like that:
el águila (
las águilas),
el aula (
las aulas)
There are many exceptions to the main rules taught in most classrooms.
Here's a
site that lists the rules (and gives exceptions to those rules). No one site lists all the exceptions.