In my opinion, it doesn't really matter whether you choose to use cotton or acrylic yarn. I've used both for baby items and have never had any problems.
When deciding on a yarn for baby items, I usually make sure to choose a yarn that will be soft and cozy against their skin and that is machine washable ... those are the factors that I consider first, rather than focusing on the fiber content of the yarn.
Hope that helps! I'm sure others will have additional insights for you as well though!
I'd probably go with a cotton/acrylic blend if I could. Cotton is harder to knit with because it doesn't have any give while knitting, but once it's made it can stretch out till you rewash it. Acrylic can get hot because it doesn't breathe. The blend doesn't seem to have as much of those problems. If you want to buy in a store like Michaels look for something like Cotton-ease.
When asking questions ALWAYS post the name and a link for the pattern if you have it.
I was given several gorgeous blankets when my son was born a few weeks ago and I have to say the acrylic and blend ones have a much nicer feel to them. I have one that is 100%cotton and it is actually rough to the touch and the drape is horrible. I will not be able to cuddle baby in the cotton blanket, it will be for tummy time.
The cotton one should soften up considerable after a couple of washes. It's okay to dry it in the machine, but just until damp. If it's laid out flat to dry right after washing, it'll be stiff, almost all fibers are.
Either would be great. I made a baby blanket from Encore Worsted, a wool/acrylic blend. Also some baby things from Kraemer Yarns Little Lehigh - they have "baby" colors and it is a cotton/acrylic blend, very reasonably priced. kraemeryarns.com.
I made a lot of baby-stuff lately.
I used synthetic fibers, cotton (just a few things), and special fibers like bamboo yarn (very soft!).
In my opinion you should not use the "staight up acrylic" stuff. When you knit that up it makes "screetch sounds" and does not feel plesant.
some wools will scratch and are no go for baby skin.
Any yarn that makes a pleasantly feeling fabric is fine for baby stuff.
Then comes the next question: Things need to be washed. And not everybody knows how to treat wool, so unless you know that it will get propper care, don't use sensitive stuff.
And what kind of piece do you make? a summer hat will be different from a winter hat. A summer dress in angora is hard to imagine, a winter coat in cotton as well. You know what I mean?
Synthetic and wool both keep warm. Good or bad, whatever the piece will be. Then they just feel different, and a densly knit acrylic might be sweaty.
cotton is breathable but can get very stiff. Thin cotton and larger needles are good, though.
My best bet is to go to the shop and feel the yarn. Then I know.
One more thing, whatever you use:
I always give the yarn label away with the piece and tie a bit of yarn to the lable as well as writing the piece on it. That helps the mother of the baby to know the treatment and material.