Mazal tov on the recent birth of your baby!
All of the methods you are interested in have an adjustment period in which irregular bleeding/staining is common. The pill (both the minipill and combined pill) usually have an adjustment period of 1-3 months until your body adapts. Some women continue to experience irregular staining on the minipill for the duration of its use. Both the minipill and the regular pill may cause unwanted side effects (beyond staining) due to the hormones. Please note that there are many different formulations of the regular pill, so even if you had a negative experience with one in the past, it may be possible to find a different type that affects you differently.
The copper IUD often has an adjustment period of up to 3 months in which irregular bleeding/staining is common. After that point the irregular bleeding usually subsides, although some women experience heavier and/or longer periods.
The hormonal IUD (Mirena) has the longest adjustment period (up to 6 months) but after that point many women experience very light or no periods at all. Some women experience other side effects from the hormones as well.
In all cases, it is important to note that every woman will have a different experience on these various methods. Some women have a difficult adjustment period, and some women are barely affected. In any case it is important to note that not all irregular bleeding/staining will render a woman niddah or invalidate the clean days. As long as you don’t experience an actual flow of blood (comparable to a period), you may take precautions against becoming niddah from any staining by wearing colored underwear or disposable pantyliners, and waiting at least a few seconds (ideally 15 seconds) after urinating before wiping. See our pages on stains and toilet paper for more details.
We recommend reading our article on choosing a contraceptive method for more details about the pros and cons of the available options, and working with your doctor to find the right option for you.
B’Hatzlacha!
This response has been updated to reflect the rulings of our current Rabbinic Supervisor, Rav Kenneth Auman, regarding waiting before wiping.