I'm actually looking into my birth control options as well. Right now my main concerns are finding something that helps clear up my skin, won't make me gain weight, and will prevent me from getting pregnant. I don't like having to remember to take my pill at the same time every day, but I think I might have some funky hormonal imbalances going on and not getting regular periods would make me paranoid, so I might be stuck with the pill.
I've only ever taken oral contraceptives, and I've had mixed experiences with them. I think it's really just a matter of finding the right pill. Last time I was on birth control, which was a few years ago, I took my sister's leftover bc that she was prescribed for a medical issue (not the wisest decision on my part, but it was free and convenient) and I felt nauseated nearly 100% of the time for the duration of the ~4 months I was taking it. On the other hand, I took Yaz as a teenager without any problems that I can recall, but it's been linked to some serious side effects, like fatal blood clots. I haven't consulted with a gynecologist yet this time around, so I'm unsure what newer medications might be available now.
The rhythm method is only 75-87% effective, by the way. I wouldn't rely on it.