The progesterone-only pill (or “mini-pill”) is usually recommended since it should not affect your milk supply. However, this pill does not allow much wiggle room for skipped or late pills.
If you are breastfeeding and do not want to become pregnant, you should consider using some form of birth control unless you meet all of the strict criteria for lactational amenorrhea. If you know you want to choose a pill as your form of birth control, you can choose a combination pill (estrogen and progesterone) or a progesterone-only pill. Estrogen has been shown in some studies to decrease milk production, but in reality, no good randomized control trials exist to definitively prove this.
The mini-pill, on the other hand, has not been shown to decrease milk supply at all, and because of this, it is often recommended for nursing women. However, keep in mind that the mini-pill requires you to not miss any pills and to take it within the same 3-hour window every day, which may be hard for some new moms to remember! If you find yourself constantly forgetting to take it (or taking it too late), then this is not the method for you, and you should talk with your doctor or midwife about a better alternative.