I agree about a good, supportive bra. My old sports bras weren't cutting it, so I ending up buying the Moving Comfort Juno. I swear it changed my life. I was wearing three of my old sports bras and still bouncing, but now I can get away with one of these.
Also, take it easy when you first start out. I was not as fast as I once was and it was rough for awhile. I felt like I had to re-learn how to run. It was rough for awhile.
I wore a nursing bra with a sports bra on top. I'd go for a jog right after LO nursed, but sometimes she'd still wake up and give DH a hard time even though I was only gone a short time. It gets easier to be away from them when they get a little older.
Start slow. I injured myself a few times in the post post-partum months doing things that used to be easy.
Re: Running & BFing
I also stuck bamboobies in my sports bra to help, because I tended to leak when I ran longer distances.
pump or feed right before you run.
take it slow.
drink a lot of water!!