You can start the mini pill 6 weeks after giving birth, i believe this is so you ensure your milk production is fully established. However i myself couldn't even bare sex untill after 3 months and even then found it painful for a while, happy to say its not painful anymore!
I'm currently using a Desogestrel mini pill, which is the 12 hour one. But i'm not 100% confortable with this whilst breast feeding due to the hormones, as a small amount passes through to breast milk, although studies have shown no effect on children, this has only been conducted until the child is 2 so there is no indication of the effects on children past this age. However i feel no other practical option for me at the moment.
My son is now 42 weeks, and i have only been taking the pill for 10 days, previous to that i was using condoms and withdrawel method, however i find condoms cause me irritation and withdrawel is not exactly fall proof.
I did also join natural cycles, this is wear you monitor your body tempreture the same time every morning before you even get out of bed, and once you have been monitoring a while you get red days (don't have sex or use other methods) and green days, which means good to go non fertile day, in principle this was great but as baby wakes at different times in the morning i couldn't get into a routine.
Hope this helps!