What you need will depend alot on your lifestyle. I agree that you'll need more covers, but since you'll have a summer baby, you can get away with putting a diaper on coverless (we prefer to use pins) and setting the baby on a waterproof pad (or fleece blanket, they're fairly water-resistant). It's alot more breathable for the hot summer months without a cover. I much prefer flats, preferably guaze, for newborns because it's much less bulky than most other diapers (prefolds/AIOs). Plus, newborns tend to pee a little alot of times, rather than later when they'll pee alot fewer times, so less absorbancy in the beginning is not such a big deal.
As for the meconium, we used Elimination Communication from day one, so all of the meconium went into the potty and not in a diaper. But that's probably a discussion for another thread...
For the first days, when you don't want to get up and run around to fetch things, I kept all of my diapering things together by the bed (well, futon for the first two weeks), including a bottle of water and stack of washcloths. That way, even when there was poop involved, I didn't have to get up and out of bed. I had a bin under the bed that I'd toss the used diapers in overnight, along with the soiled washcloths.
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