I've cloth diapered 5 kids on the cheap- of the systems you mentioned the only ones I have much personal experience with are Fuzzibunz and some hand-me-down Bumkins covers, not AIO.
I liked the Bumkins covers, they do have the sharp velcro edges though so if baby gets to have a really fat belly that overlaps the diaper when sitting, they are not as comfortable as the Fuzzibunz. And those are the covers, not the AIOs.
I would not call Fuzzibunz an AIO system either. They are pocket style diaper covers that you stuff with an insert, or you can use them like normal diaper covers. I have been very pleased with them for older babies! They can also be big money savers as you don't have to stuff them with a premade insert, you can use a prefold, old dishtowels, rags, you name it. I have also been pleased with how well they've lasted in the wash and as hand-me-downs, granted my kids use them a little less than someone who was cloth diapering full-time and not doing elimination communication as well. We use elimination communication or EC, along with cloth diapering. EC can reduce the size of your diaper investment and the number of poops that have to be wiped off the baby's bum. http://www.diaperfreebaby.org/ EC can also speed toilet learning- my youngest is not yet 21 months and does all her poops and about 50% of her pee in the potty now, my other daughter we did this with was using the toilet exclusively by 22 months- my son took longer and wasn't reliable until after age 2.
I'm also not sure I'd like the Fuzzibunz as well for a newborn, since they poop so much more frequently- you would need a new diaper cover for every poop- I think you'd need at least 16 newborn size covers, although that's not a huge investment if you figure you'd need at least that many AIO's!
HTH a little!
Also, unless you really want to spend significant moolah- if you buy AIO's you are probably going to spend a lot more than you would for covers in different sizes and prefolds that your daughter could use throughout baby's toilet learning.