It all depends on the woman. You can talk with your gynocologist to find out what she thinks will work best for you.
I hear a ton of horror stories about the Depo shot, and even one of my teachers commented you have to have just the right make-up for it.
I take the pill to great success and no side effects (when I had some start at random, I changed the time I took my pill and was fine), so if you can remember to take a pill daily at the same time daily (I set my cell phone alarm), the pill may be good for you.
A couple of my friends have the Mirena (an IUD) and love it.
Like I said, it just depends on you and your needs. Talk to your gynocologist about what you're afraid of as far as side effects and she'll help you come to a conclusion that's right.