And the winner is…
Pre-fold with diaper cover
The pre-fold with cover diaper system is the best one. Feel free to argue with me about this, but here’s why I came to this conclusion:
1. All-in-ones are too expensive. You have to use a brand new diaper every time, making for a very bulking diaper bag during outings. They take a long time to dry after washing. Some require special washing instructions. They are extremely hefty on newborns because of a lot of unneeded fabric lining the inside.
2. Pocket diapers are like pre-folds with covers only with an annoying extra step. You have to “stuff them.” And you have to use a new cover every time because you’re stuffing the insert behind a lining. Let’s just skip that step and move to …
3. Pre-folds with covers! Since you can take the soiled or wet pre-fold out of the cover, you can just use the cover again–you only have to change the cover if there was a major explosion. You can’t mess up a pre-fold laundering it since it’s just cotton, and covers are typically just as easy to wash. And it’s WAY CHEAPER than the two alternative forms of diapering. Buying a leading brand all-in-one diaper costs about $432 for 24. My stash of diaper covers (6) and pre-folds (24) only cost $150. Even after I add 24 more pre-folds a size up, the cost will be $216. Almost ‘perzactly half the amount of all-in-ones.
eclecticmothering 
Do you use these with EC? I was convinced at first, that this is the best system, for exactly the same reasons you’ve listed here. Except I found it just took too long, especially since we are ECing, and i take off the diaper about a billion times a day…. But then again, i was using flats, not prefolds. Do you use a snappy with prefolds or just lay it in the cover…?
Just lay it in the cover. Since we don’t have that many blowouts, I can reuse a cover. Yes, it is a pain to get the diaper off and on, but it’s doable. Sometimes I use a diaper belt instead on a larger prefold.
I wanted to tell you that I’ve finally got ahold of some good covers which actually fit! So I’ve been using them with flats for about a week, and it’s great. I have to fold the flats first to get them the right size, but I’m not using any snappi either, and it works fine even with EC. I have 4 Ao diapers, but I almost like the flats better since They are easier to wash, dry in about 20 minutes in the sun, and are super cheap so I’m not worried about”ruining” them. The AIO’s are so nice and beautiful that I’m almost afrad to put them on her in case I miss a poop. (I do catch most of the poops though.)
What brand are they?