I'd actually just use some sort of soft acrylic - there's lots of "baby" yarns out there - and the reason being is that they can be thrown in the washer and not hand washed (in the case of 100% cotton or wool)
I appreciate all the advice.
My friend finds most wools very itchy. I don't have much experience with babies, so I wasn't sure if wool would irritate their tender skin.
I also didn't know that pure cottons and wools have to be handwashed!
There are many cottons and some wools that can be machine washed and dried. Wool yarn that can be machine washed/dried is called "Superwash." Also, merino wool is very soft, much softer actually than most acrylics.
Generally acrylic is not a good choice for socks because it tends not to hold its shape well and doesn't breathe, making feet too hot and sweaty. However, that may not be as much of a consideration for babies who are not walking around yet.
Of the various baby socks I made for my grandchildren, my daughter prefered the cotton with elastic for when they are tiny (and I even made some out of cashmere :lol ) She said they stayed on better than anything she could buy or was made.
I used the Elann Esprit yarn, but I understand it's almost identical to Cascade fixation.