I don't think you are supposed to use anything internally for postpartum. I have a DivaCup but am planning to use cloth pads until the PP flow is over and my regular cycles return. I think one of the issues is that menstrual cups rely on your vaginal muscles to hold it in place and things are not quite the same in there until you finish healing.
I just wrote a big long post in Mindful Home about cloth pads so I won't repeat myself here, but basically I listed some of the places I got my pads from. I think right now my stash has 10 overnight/PP size pads, 4 heavy, 7 day pads, and a whole stack of lights/liners (probably around 15). My light pads have been getting a workout even in pregnancy for everyday discharge kind of stuff. I'm currently debating if I should get a few more heavy ones, it's tough because it's my first baby so I don't know what kind of flow to expect and I know it varies by person.
Some mamas use infant or preemie prefolds just tri-folded in their undies, and I guess as long as you change frequently you shouldn't leak through. My pads have fleece backing which seems to be a very good waterproof barrier, I think it is definitely more breathable than PUL.