Pocket fitted diapers are a really great first style of diaper to sew. Just use recycled absorbent fabrics or some inexpensive flannel and sew a few for practice before you dive into things like PUL, wicking jersey, or expensive absorbent fabrics like bamboo or hemp fleece. :)
I've made these two variations out of some flannel scraps I had leftover from an old project and a recycled cotton hospital blanket that my son was sent home with after a surgical procedure a couple years ago.
You can make them with or without closures (snaps or hook & loop), and you can stuff them with pretty much anything. You can utilize an old microfiber insert or shop towel, old t-shirts folded up, a prefold, small towels or washcloths... pretty much any absorbent item.
*For a pocket fitted or any back leading edge pocket, you'll want to leave a bit of the outer fabric longer in the middle to allow for the back elastic casing. It will be folded inward and sewn to create an elastic channel later on.
install your elastics and sew down the edges of the pocket opening securely. For a turned diaper, you would then do your top-stitching as well.
Here is a closureless T&T style pocket fitted diaper.
The completed serged pocket fitted diaper next to the T&T style.
Showing a fold-over rise:
These diapers were made using my M-L Fitted template.
All my diaper templates can be downloaded free here: http://prefold2fitted.blogspot.com/2012/10/online-free-downloads.html