This is our system. The diapers have been very durable and continue to work well. I like to buy them from Wildflower Diapers or Diaperware.
So, here goes.
I think disposables are the easiest for the first few weeks because the babies are so small. Even the trimmest cloth diaper seems huge on a newborn.
Pocket cloth diapers can be costly to buy upfront ($10-25 each!). You might not want to buy the super fancy diapers in the smallest sizes because 1) they grow out of them so quickly and 2) they need 8-12 diapers per day.
For the first few months, we used cotton prefolds (4x8x4 ply, unbleached Chinese prefolds in the infant size) with diaper covers (Either Bummis or ProWraps). I think we had about 18-20 prefolds and 6-8 covers. We washed these every other day. If you have diaper rash problems, you can lay a piece of fleece over the prefold in the diaper and that keeps the baby's skin drier. I actually like diaper pins because I think they make the diaper fit and stay in place better. Matt was not a fan of pins, so he just put the diaper in the cover and fastened the cover. Didn't use the Snappi, although some people love it.
Older Infants through Potty Training:
Once the babe can fit in size mediums (for Mollie this was about 6 months, for Lucy this was about 3-4 months), we started using Fuzzi Bunz as our main diapers. I have 16-18 of these in size medium and wash every other day. The mediums fit Mollie for a very long time (until 18 months) and then we switched to size larges and didn't need nearly as many (10-12). These lasted Mollie through potty training (she was ~2.5 yrs); we have yet to see how long they will fit Lucy.
Fuzzi Bunz are pocket diapers, so you can stuff anything inside the pocket to increase the absorbency. I use an infant prefold and a doubler or piece of terry cloth. Microfiber inserts work well as doublers, but do NOT work well by themselves. I made a few hemp jersey inserts that are very trim and absorbent. These are my favorite inserts, but since we already had all the prefolds from the infant stage...
When the baby starts solid foods, we start using diaper liners. Ours are from Imse Vimse. It says they are flushable, but I routinely throw the pee-only ones in the wash with the diapers and they last through 3-4 washes!! I don't flush them!! If the poop is solid, you can just shake it off into the toilet. If it's not, sorry to say, I throw it in the trash. (Yes, I know you're not supposed to do this but at least I'm not throwing like 8000 disposable diapers in there too!)
Laundering and other info
We use a regular trashcan with a pail liner and put the dirties in there. I just dump the whole thing in the washer. First, I do a cold rinse/spin. Then I do a hot wash/cold rinse using Planet detergent and a little added washing soda. If there are still visible bubbles after this cycle, I do one extra rinse. I always line dry the covers and usually throw the inserts in the dryer (because it's so darn humid here).
I like diapers with snap closures (Fuzzi bunz) because velcro tends to snag on everything in the laundry. But, the velcro are a little easier to use, so it's a toss up. The velcro pocket style diapers are newer and I only have tried two. I have one bumGenius adjustable one-size. Lucy is on the largest setting right now, so unless she miraculously starts potty training at 9 months old, I think the one-size diaper will not fit her all the way through potty training. The other velcro diaper that I like is a Dry-bees. The sizing is very generous so I think a size medium will fit for a long time.
I don't recommend All-in-one diapers (AIOs). They take FOREVER to dry and I never felt like they were getting thoroughly cleaned.