I love FAM, and it works well if you have an excellent understanding of it. I flat-out refuse to put more hormones into my body after what taking the birth control pill did to my PCOS. I went from having a relatively mild case--only symptoms being occasional irregular periods and acne--to a very strong case with pretty much each and every symptom there is. And the only thing that changed was I was on the Pill for a while, then came off. And from a faith standpoint, I feel much more comfortable with FAM as well.
I don't recommend counting your days to anyone as a form of birth control. That's essentially what the rhythm method was, and the Catholic church abandoned that because it didn't work for more people than it did work for. They use a form of FAM now (FAM & NFP are very close to the same), and you can get classes in it from the Couple to Couple League.
It is a little confusing to begin with, but I found TCOYF to be an excellent explanation of it. I have said before on this site (though not this particular forum) that I credit the existence of 2 of my 3 children to TCOYF.
Anything natural is probably not going to be endorsed by your doctor, of course.

But I have found that natural family planning methods in general are better accepted outside of the United States. I recall after having my first daughter reading in hospital-provided literature that NFP was essentially as effective as
no birth control...which of course is nonsensical. But that very same day I had a doctor tell me that there's no such thing as lactational amenorrhea, which is also nonsensical. And at the very same time I have found in my own research that natural methods are recommended by international sources, especially LAM. So, well, I don't rate too highly the opinion of someone who's writing with a Pfizer pen, KWIM?