Hi J.!
I had the Mirena IUD inserted at my 6 week pp visit, and also had one prior to TTC my daughter. The insertion of the first one caused me to have a vagal response (I got nauseated and faint and had to have my husband pick me up from the OB/GYN's office), but with the second, I didn't have any problems on insertion. I spotted for 3 months after I had it put in. When I got my period back at 11 months pp (thank you, breastfeeding!), I had HORRIBLE back pain and cramping. I was ready to have the IUD taken out, but my doctor told me it was probably just a change in my cycle and that the first postpartum period could be severe. I stuck with the IUD, and I have had only slightly worse cramping than my pre-baby periods. I also only spot, where I was a heavy flow kinda girl previously.
There's little risk of supply drop with the IUD, because the hormones it releases are local to the uterus, therefore not a lot of them get in your blood stream. Your other options are the minipill and the depo shot. The minipill can be effective, but you HAVE to be able to take it at the same time every day and you CAN'T forget a dose. Since it's lower dose hormones, you have to be consistent so the level stays high enough to prevent ovulation. It can also reduce milk production, in some women drastically. The Depo shot is very effective birth control, but can also reduce milk production drastically. It's also non-reversible for 3 months, so if it does decrease your milk, there's nothing you can do about it.
Anyway, I'd recommend the Mirena. I've been fairly happy with it so far, and I've had it for about a year and a half this time around.