Welcome to the NFP/FAM board!

The ladies here are super helpful and friendly.
It's my personal opinion that if you can avoid hormonal BC, do it. I've just come off of the pill after 5ish years on and off, and I feel much better already. I read about charting and FAM-style birth control for a long time and then finally took the plunge and invested in the Taking Charge of Your Fertility book - it's a GREAT place to start if you're new to things. The author has a website too where you can read about some of the basics:
Welcome to Taking Charge of Your Fertility
The book is useful whether you plan to use FAM as part of your birth control or to try to conceive. I would definitely recommend poking around her website and looking into the book, if you like what you see. I'll be honest and say that I (and others) have found it pretty overwhelming at first, but with a little bit of time it starts to make a lot more sense. It's just a lot of information all at once.
TCOYF approaches FAM from what's called a sympto-thermal FAM theory, which means that it talks about using a combination of waking temperatures and cervical fluid (your major fertility indicators) to identify ovulation (as well as cervical position, although this one many people find a little harder to interpret and the book considers to be an optional indicator). I (and a couple other members) use this type of FAM and feel comfortable with it.
We also have several ladies who practice (and a couple of whom are experts in) a method called the Billings Ovulation Method, which (to my understanding - feel free to correct me if I say this poorly!) only uses cervical fluid as a fertility indicator. There are other minor sub-categories of FAM out there, but those are the two that you'll find most commonly on this board. I'll let one of the other ladies leave a link or further explain BOM, if you're interested.
Personally, I think they both have a lot of merit and are both quite accurate if used correctly - FAM is definitely one of those things that you get out of it what you put in.

Whatever you feel most comfortable with would probably be the best place to start, IMO.
Regardless of which method you end up using, a good understand of the ins and outs of the menstrual cycle and the fertility signs would be a great place to start. I found that TCOYF gives a pretty thorough (but concise) explanation, both on the website and the book. I would also advise that if you don't want to TTC, you should be very disciplined with birth control if you're comfortable with using it (condoms, spermicides, etc.) and use it ALL the time for your first cycle or two. The downside is that those things do alter your cervical fluid which makes it harder to interpret, which is a pain while you're first learning, but it's an option. Abstaining from any genital contact for a month or so is another way to a) ensure you don't conceive unexpectedly and b) keep your cervical fluid clear while you're figuring out what the different types/stages of it look like for you.
Expect some craziness post bcp.

It's normal! Most women aren't 100% textbook even without having been on hormonal birth control. An actual certified instructor can be a huge help too, if you can find some nearby. We have a member who is an instructor, actually, and if you would be interested in that I'm sure she can help you figure out how to do that in your location.

You certainly don't have to use one, but it's my understanding that they can be a fabulous resource, especially while you're first learning.
Be patient with yourself, have faith in your body and definitely make use of this forum and other resources while you're learning!