Also with the depo shot, you may or may not get your period. There are no guarantees. Some women have there period for the whole three months!!! So do not pick depo for that reason. Your doctor will not put you on anything that he/she feels you should not be on, but you definately do have a choice as to what type of birth control you go on.
I would highly recommend the pill at least as a starting point. If you get the shot and have a bad reaction, you just have to deal with it for three months. But if you get put on a pill with a bad reaction, you can switch to a different pill that does not bother you.
If you do not want to mess with your hormones there is always the diaphram. But whatever you choose, don't forget to use condoms!!!