We have a variety, which seems to be typical for cloth diaper users. You don't know what will work best on your baby, what you'll prefer, etc., so it's probably best not to stock up with exclusively one kind.
That said...
We are currently using prefolds with covers. Most of our prefolds were bought secondhand from a local diaper service/cloth diaper store (previously used for the service, so higher quality/more durable than regular prefolds!); I also bought a dozen OsoCozy brand from Amazon. The covers are a mix of Bummis and Thirsties. I bought some (again, secondhand), but most were hand-me-downs from a friend. They have been great so far, only 1 or 2 very small leaks, and no poop blowouts.
We also have a bunch of pocket diapers. I don't remember off the top of my head what brands - a few Bummis, I think, one Best Bottom, 3 Oh Katy!'s, idk what else. They're a mix of hand-me-downs, secondhand purchases, and some that I bought new when I found good deals. We haven't actually used any of them yet; Baby Tofu is only 3 weeks old and doesn't really fit them well yet.
For wipes we are currently using the disposable wipes we got as gifts, but I have 2 dozen GroVia cloth wipes that we will start using in a couple of days, when the disposable ones are gone. Our diaper pail is a basic plastic lidded trash can from Target, with a Planet Wise liner.
Most of what we bought new came from Amazon. We had a registry there as well, and they have a good variety of brands. Plus they offer a 10% "registry completion" discount (15% if you do Amazon Mom), so you can get a discount on stuff you still need after a baby shower.
A couple of the pockets came from Zulily. My favorite is one with a Dr Seuss print.
I would definitely recommend getting as much as you can secondhand. Good quality cloth diapers will last through more than 1 kid, and you can save a lot of money this way. Plus you don't have to do all the prepping. ;)