Hey welcome Munro.

You should be fine in Melbourne without a dryer, as long as you've got a clotheshorse - especially in Summer! I will concede though that a dryer does take a bit of pressure off in winter.
It really depends on how many nappies you have all up, and how often you wash.

GreenKids pocket nappies are great, I've not used them on a newborn though, I've used BumGenius pockets on a newborn and thought they were great! I imagine GK's would be a bit bulkier on a newie.

For bamboo nappies, for a newborn, I'd be leaning towards bamboo terry (like Bambineo or Tots Bots Bamboozle) in size 1, they'd fit for quite a while. Bamboo fleece, like with Baby BeeHinds is great, but bulky on a newborn, where terry is trimmer and slinky. I'd say terry dries faster too?

Many people with a newborn just fold up a bamboo/hemp trifold (piece of material that folds in 3) and sit it in a snug PUL cover. Many others (as Maz said) use prefolds, which can just be lain in as well, or be secured with a snappi (or pins, but a snappi is easier!). Prefolds are great, they'll dry really quickly, easy to wash and pretty easy to use, not to mention that they make good size spit/cleanup rags later.

Keep in mind also, while pocket nappies are great if the fit is good, a fitted/prefold and cover will give you a bit more peace of mind against exploding poo - small baby poo can come out with some force at times!

Like Sammi, I'll keep thinking on your criteria, you fussy person you. To be honest, the easiest way to meet that criteria might just be to make your own...can you sew at all?