I use regular stuffing for the core of any felting project I start. The more cottony feeling the stuffing is the better. I use Morning Glory stuffing, which if any of you have used it you know the texture is different from box to box. When I get the more slippery stuff I make a quick run over the finished shape with a lighter to shrink up stray bits that would otherwise show through the final color layer.
For the color layer I will use a couple of different things. On rare occasion I'll actually get to use roving (I have a stash of angora from a a friend I made one thing and it was so soft and wonderful I couldn't think what would be awesome enough to use it again) but for the most part I use yarn or felt. They both need to be shredded back into rough fiber before you can use them so there's a lot of elbow grease involved.
Some of the fluffier chunkier yarns, like Lion Brand Homsespun, are really easy to shred, you just have to find the thin thread that's wrapped around the thicker fluffy strand and unwind it. The thicker strand will pretty much fluff apart.
Otherwise I just bust out the scissors and get to work like I'm curling a party ribbon.
I don't suggest using cotton, it shreds readily but doesn't felt worth a damn.
For the felt, you don't really want to use the cheap stuff you find in most crafts stores by the sheet. Either go by the yard or get the really good stuff on Etsy. I know not terribly money saving to tell you to go buy stuff, but it's still cheaper than roving and if you use felt at all it's a win-win.
Same method when shredding the felt, though once it gets started you can just pull it apart with your hands and save your thumb a bit of ouch from the scissors pushing up on it.
And that's what I do every time I felt something. Speaking of which, here are some of the projects I've got going on right now.
My sexy bearded lady, available here
Excuse me Mr Lion, I seem to have lost my hat
One day I'll get wings and be finished
He just needs weights on his barbell and his signage and he'll be ready to go