There are so many different kinds of wool, and some are really scratchy. Get sweaters that don't feel so scratchy to you. Merino wool is really soft, most people wouldn't even believe it is wool. I have some really scratchy sweaters that I got when I was first trying to make wool covers, but now I will not use them since I have seen the difference with soft wool.
And no, it doesn't have to be 100% wool. If it has a blend of cashmere, silk, angora, mohair, or some other kind of animal fiber, it will be great. Avoid cotton because it will absorb. If it is blended with nylon, acrillic, or some other type of synthetic, it will still work too. You just might have to wash it more often because the synthetic fibers don't have the self-cleaning properities of wool. I've heard that as little as 20% wool content will work, but I usually try to stick close to 100%. if it is 90% wool, I use it with no fear.
To felt wool, wash it on warm or hot with detergent, then throw it in the dryer. You can wash by hand if you want to conrol the felting. Something I like to do is throw it in the washer for a short wash in warm water. If I think it needs to be thicker, then I will wash it again on a longer wash in hot water. But you don't HAVE to felt it. If the sweater is already thick, you might not want to felt it because it may get WAY TOO THICK to use. Just be sure you lanolize the cover well if you don't felt it. Also be careful when you cut it out, non-felted sweaters tend to unravel.
Knowing how thick you want it takes a little practice and trial and error.