Types

Wool-

Wool covers come in two forms knit and wool fabric. Of those two you can have either pull on covers which require the use of snappis if you are using a prefold or snap/velcro ( APLIX) covers where you can just fold the prefold in and snap it on with out the use of snappis or pins. 

I love wool. It's more breathable than pul and I find it a more comfortable solution. 

Caring for it is a breeze- all you have to do is once or twice a month wash your wool with wool wash in luke warm water and pad it down with lanolin ( about a pea/dime size glob rubbed on your hands per cover . Lay it out to dry ( or line dry) and your done till it starts to not smell nice usually 2 weeks - a month for me because I rotate my covers. Or if it gets soiled with poo.

PUL-

These are great for newborns where you might get poo on your cover a lot. I choose mine with leg gussets so it catches anything that leaks out of the diaper so it doesn't get on you or the babies clothes. Once soiled just wipe it out and reuse, or toss it in your wetbag with the soiled diaper.

My personal favorites are Proraps colors, Bummis Super Brights, and Thirties These have held up for me and they have great quality control.

I am usually not a big fan of APLIX ( velro) but some of these come in snapped variety. Honestly it's a personal preference. Some like the ease and quickness of the APLIX. Some hate the fact it snags on things and gets caught up in the laundry. 

Fleece/Acrylic yarn-

These covers have the look and feel of wool but the ease of washing of PUL. You can just throw it in with the diaper wash. Dry in the dryer with a dryer sheet as that helps it repel liquid. 

You can actually knit with acrylic and it will work as a diaper cover you just have to wash it every other time it's worn or until it starts to stink.