Always use cotton as a first layer, because you can just put it in the laundry. Cleaning my woollen coat is more difficult than changing a cotton shirt underneath it.
Also: most “wool” is polyester because it’s like 10 times cheaper.
Cotton remains damp after you sweat and eventually also stinks of sweat. It's not a good base layer in cold weather. A lot of merino wool products are easy to clean and maintain. I have never seen polyester called wool.
This is good - potentially even life saving - advice if we're talking about doing serious activities outdoors. And in that case, even wool is probably best replaced with synthetics that are lighter and dry quicker when wet.
For around town, though, a cotton base layer and wool works pretty well.
I must side with the other replies to your comment.
I have been wearing cotton as my top base layer for a while, and it is not great at staying dry or drying out while damp.
I'd certainly choose it over any synthetic fabric, but once you go over that low mark, just about anything is better, e.g. wool, linen, help, silk, etc.
Also: most “wool” is polyester because it’s like 10 times cheaper.