You can adjust a BumGenius (by even folding down the velcro at the front and just fastening by joining the two tabs) so that it goes really really small! We've used them from super young, like a couple of days old, and they've been great! We used them for Riv too as a newie, and we never had a leak with them!

What you get really depends on your budget. I find that by about 4 weeks, babies are starting to reliably fit a size small, and fit nappies like Baby BeeHinds and other fitteds (and BumG's, if they haven't been working before for some reason).

My ultimate newborn money-no-object stash would include nb Whiz Kids (rare as hen's teeth, I was lucky enough to snaffle Willow's), BumG pockets and size 1 Tots Bots Bamboozles.

My realistic newborn stash was a combo of BumG's, prefolds (excellent spew rags after), and sposies (while catching up with washing). And a few size 1 Tots Bots.

At 6 weeks, we fit into BBH Bamboos, size 1 Tots Bots cottons, and size 2 Bamboozles (being bamboo terry, they're a bit more slinky and slim, though still a bit bulky this young), BumG's, prefolds, small BerryPlush, Hautes (I've heard some like these even better than BumG's for nb's)...I think that's all so far...

Unless money's not an object (in which case, go to town with nb sizes, awesome!), perhaps go mostly for ones you'll get some wear out of, since, while fitting nappies are sooo handy in those first few weeks, they grow so quickly that nb nappies aren't really that economical.