I don't have any all-in-ones like the bambinex so can't advise on them. I have all fitted nappies (selection of tots bots, fuffles, little lamb, motherease onesize etc etc) with separate wraps.
One thing I would say is to get a few to try out at first then order a full set if you like them. I have found some of the nappies to be very small fitting. My baby is heavy for his age but he is not "big" if you know what I mean, he is more solid. For him any so-called birth to potty nappies would last nowhere near potty training!