My mom told me the same thing, but our expert lactation consultant recommended against it. It's the stretching of the nipples that causes that initial discomfort anyway, which is something rubbing won't prepare you for. I agree that breastfeeding gone awry is a totally different story. I'd highly recommend that any pregnant woman line up a good lactation consultant and/or take a class before the baby comes!
As for bra sizes, I got softer, stretchier bras that allowed for some expanding (and later shrinking) as I transitioned during pregnancy and nursing. Then once my breasts settled into a size after nursing was established, I got more fitted nursing bras. This method worked well for me. I think I went up a couple cup sizes and a band size total.
Agreeing on everything you said! Line up a Lactation Consultant before you have a kid. Even if you think you can handle it.
And yes on the stretchier bras. If I recall, my main bra post-natal was a nursing sports bra that stretched and shrunk as my boobs allowed. Not to mention, the fitted nursing bras are harder to fold down and keep from whacking the baby in the face every couple seconds. Softer sports bras were more comfortable.