After my son was born, I had the Mirena IUD put in. It's smaller than the copper ones and it has a small amount of progesterone that's emitted, locally, to the lining of your uterus.
I had good luck with it. It was uncomfortable to be inserted. You have to wait until your first day of your period (that's when your cervix is the softest and it's open slightly - and you're most likely not pregnant). They insert a small, plastic tube into your cervix and push the IUD up. It's tiny and after it's inserted, you don't feel it at all. The insertion takes less than 5 minutes and feels very crampy. It's over quickly though.
In terms of side effects, I had some breakthough bleeding for the first 3 months or so... just spotting really. Then, nothing. I don't think they recommend Mirena for women with diabetes or heart disease. The only weird thing with the Mirena is that you don't get your period. You still ovulate, but since it has the progesterone, the lining of your uterus doesn't get thick enough to "slough" off. I didn't really like that part, but it wasn't so bad. I liked the fact that I was still having regular cycles - ovulation-wise.
Since I had pre-e, my doctor suggested that I stay away from combination oral contraceptives (with estrogen). This seemed like the best alternative. I think if I was going to have another one (IUD), I'd get copper this time. Even though I didn't mind the Mirena, I don't really like the idea of synthetic hormones flotating around my body. I was happy with the concept of the IUD though. It's very easy - you don't have to remember to take a pill, you don't feel it, you don't have to stop to put a condom on and it allows you to be spontaneous without worrying about getting pregnant. You can also keep it in for 5 years. I think you can keep the copper one longer.
I had my IUD taken out in May and it was very very easy. They just pulled the string hanging out from the cervix and it was out in less than 5 seconds -- and there was no pain.
Good luck with your decision.