DIAPERS THAT NEED A COVER:
Prefolds- This is the original cloth diaper that was used by my parents generation and prior generations. They need to be wrapped, pinned and covered. This is the most economical option of the cloth diapering world. These run anywhere from $1-$5 a piece. They usually come in dozens, and are made of either bleached (white) or unbleached (natural) cotton, also know as Chinese or Indian prefolds. They must be washed several times before use to prep them, in order to increase the absorbency.
Fitteds - These are similar to disposables, but they require a cover. They come either sized, meaning you need to change sizes as the baby grows, or one-sized, with snaps that enlarge the diaper as the baby grows (can be more bulky when the baby is younger). A one-sized diaper can usually last from newborn stage to potty-training (most are 10-35lbs), so they are be more expensive. These diapers range from $10-$30 a piece.
DIAPERS THAT DO NOT NEED A COVER:
Pockets - A diaper cover that has an opening for an insert, made of bamboo or hemp (or a number of other fibers) goes in the pocket. People sometimes use prefolds to stuff them, for nighttime or heavier wetters. When the baby soils the diaper, the insert should be removed and the whole diaper needs to be washed. These also come either sized or one-sized. They range in price from $12-$25. The outsideiof this diapers is waterproof, so it can go cover-less.
All-In-Ones (AIO) - These are the most like disposables (and usually the most expensive) cloth diapering system. Everything is sewn in, no inserts needed, but they can be added as "doublers." When it's dirty, the whole thing goes in the wash and a whole new one goes on. Once again, they come sized or one-sized. They range from $15-$30.
All-In-Twos - These are similar to AIO but they have either a snap in or lay in soaker . The name All in Two arose from the ability to get two uses out of each diaper. When your child pees, theoretically you can remove the soaker and replace it with another if the shell did not get wet. AI2s also have a much faster drying time because the soaker is external.
Covers - There are a few different types of covers: the wrap- this refers to covers which can be velcro or snap closing, that fasten in front, like disposable diaper (most popular); the side closing- these are usually snap closing covers, but there are some side-aplix covers out there; and pull-on- which is exactly what they are, they can only be used with fastened prefolds or fitted diapers.They also come in a variety of fabric- polyurethane laminate, fleece, and wool (which a lot of people consider to be the ultimate cover material).
Doublers Inserts, and Liners - Doubler are used for extra absorbancy and a lot of people uses these for naptime or at night. Liners can be washable or flushable, this is what some people use instead of full cloth or full disposables. Inserts are used with pocket diapers and can be used by themselves or as doublers.
Snappi and Pins - These hold prefolds or fitteds together.
I currently have a little if everything. Mostly prefolds, fitteds, and covers. I have a stash of the FLIPs system but that will be for after she hits 10lbs or so. I also have some pockets and AI2s for when she is ready for daycare. I will updated you with what works for us as time goes on.