When it comes to newborns, my theory goes like this. They need to be changed ALOT at this time, but, don't necessarily get every diaper very dirty. And the newborn size doesn't last very long, so renting them comes out about dead even and buying them would take five years to get your money back (assuming you buy a pocket/AIO newborn type, obviously covers and prefolds would be cheaper). Even with prefolds, its not that big of a money saver to me and is significantly more work at a time when I need every break I can get. By watching and using coupons, I stock up on about a month's worth of paper newborn diapers ($40 or so if you buy them at full price from a brand name), and its wroth it to me. Then they should fit into a small prefold and I use disposables at night until they fit the pocket/AIOs.
As to cloth diapers, I like them all for different reasons. AIO is more convenient, but takes longer to dry unless you live in Arizona and its summer. I have mostly pockets and love them, they also can be over-stuffed to get a different fit and they seem to be leak-proof if you can get the fit right. I use bumgenius in several different types, and the thirsties duo: these brands were chosen because, where I live, you can get them for less than half price used on craigslist. I bought a few here and there as they because available at a good price in good shape. Some need the elastic/velcro replaced after the first 8 months of use by me, but that's a cheap/easy fix. If I could just wave a magic want I would probably buy an AU brand like HH or rumperoos, but those are pricey in the states. Even half price they cost more than new BG or fuzzibuns. I've heard good things about every one, so I just bought what looked good to me and figured I'd resell them myself if it didn't work out.