I have been on the pill for about 5 years now. From things that my doctors have told me is, birth control an actually cause cysts, not help prevent them (but there could be studies that show they help in preventing them, be more clear in asking your doctor). There are always chances of every risk that they warn you about, but that happens in a very small percentage of women. I don't think hair growth has anything to do with birth control.. Unless you have higher testosterone levels.
I would advise getting on the pill. Especially since you are sexually active. And about your periods, if anything, birth control will help with that. Before I got on the pill, mine were completely messed up, which was the reason I started taking them. I personally don't trust condoms by theirself. They're great for prevention of std's (always use them, even if a partner tells you they're clean). But I would always use a back up method.
With not using birth control, your chances of becoming pregnant are obviously higher. Not being on them wouldn't increase you becoming more fertile.
If you don't think you could remember taking your pill everyday, there are other forms of birth control. There is the depo shot (i think you get it every 6 months) and there are other things like the patch that you put on once a week. If you're not ready to take care of a child, get on birth control.
I hope I helped with answering your questions.