Oh..the cloth diapering world is a wonderful and addicting place!
I agree with many here about prefolds and covers. We have used this system (versus the AIO or fitted) with DD for 2 and a half years. Only once has she really had a rash...it was minor...and went away quickly with some fresh air and some pure lanolin. I am so passionate about CD for so many reasons, but for one it is soooo much better for your child...it kills me to think of all those chemicals against baby's sensitive skin.
We use Indian prefolds (unbleached cotton) in a 4:8:4 ratio of thickness. These numbers refer to the number of cotton layers that are shown together (4 layers on the outsides and 8 layers in the middle). You can get them in 4:6:4, 2:4:2, etc. A less absorbant prefold would probably be fine for a newborn, as they tend to pee a lot and not in great quantities. Then as your baby moves up in sizes, you may want to get them in thicker layers.
For covers, we use proraps, bummis, wool ones from Imse Vimse, and wool ones that I knitted myself. Wool is incredible and well worth checking out.
Every child comes with a different shape, and so not all diapers will work for your child. Some may leak a lot, while others will seem perfect. At first, I would just get what appeals to you or what someone passes down to you. Then, go from there.
I don't like AIO diapers as much, because they are more expensive and I think they require more laundering. Yes...they are fluffy and cute...but I'm really not sure they're worth it. With prefolds and covers, you don't really have to wash the cover every time, but with AIO or fitted...you don't have a choice. Everything goes in the washer, every time.
Prefolds and covers always just seemed more simple to me. I like the functionality of them, and in 2 and a half years, I have always managed to clean the diapers fast enough that we have NEVER had to use a natural disposable out of desperation. The other mamas I know that use AIO, almost always carry disposables with them too. The laundering can just be too much when you are busy.
Washing cloth diapers is a whole other topic, and if you are interested...you should start a new topic about that.
I buy my prefolds and covers at clothdiaper.com, greenmountaindiapers.com, and from a little cloth diapering store we have around here.
I think I'm gonna try some flats this time around, for something new. I just never bothered to learn how to fold them up!

Good luck and have fun!