I prefer fitteds to prefolds for newborns, they're a bit easier when you're bleary eyed and fumbling in the dark! Of course flats are a bit more customisable than fitteds (assuming you fold them around baby rather than simply folding them into a pad - I wouldn't recommend that with newborn poo!) so if you wanted flats, I'd go for terries as they wash and dry better than prefolds and are even more customisable. I think Birdseye flats have more or less the same advantages as terries, if they're more common where you are.
We used newborn nappies (mostly fitteds, some AIOs) for about the first month then gradually switched to bigger nappies. It depended on the brand really. There was one brand of OS nappies that fitted my newborn at 4 days old (didn't think to try if before that) and she wasn't a giant baby (7lb4oz at birth), most started fitting somewhere between 3 and 6 weeks old.