In my experience they do tend to run small. They also go on US sizing, whereas most non-nursing bras tend to use UK sizing. That really doesn't come into play until size DD+. You also can't get nursing bras as big as regular bras.
I do recommend waiting until month 8 or 9 of pregnancy to buy nursing bras. I went up a full cup size right at the end. You'll probably also go up a band size or two, but bra extenders are fantastic to help with that.
If you're anything larger than a C or D, it will be tricky to find good nursing bras (or really, good any kind of bras) in a store. I recommend Bare Necesseties - you can shop online, returns are easy.
I've found that unless I'll be nursing in front of other people - ie, we're going out or having guests - it's easier for me just to take off my shirt and bra to nurse. Having large breasts, it's a two-hand affair to get a boob out, and they're just not as supportive or well-fitting as my regular bras.
One great thing for nighttime is the type of bra that is like a halter top. It's one triangular panel over each boob, and you just pull it to the side. Mine is too small for me, but doesn't cut in. It provides enough support to get up and change diapers, etc. in the middle of the night, but doesn't get in the way while I'm sleeping.
Overall I'd recommend getting just a couple nursing bras to have, then once you figure out what's working for you and what your size will ultimately be (I went back down a band size a few weeks after delivery), you can buy more if needed.