You may find a dedicated sweatshirt/tracksuit fabric section in your fabric store of choice. If you don’t, just head for the knitwear section and look for a thicker comfortable knit fabric.
As far as fibers go, you can go all cotton, or opt for a poly or acryl cotton blend.
Make sure to pay attention to the inside of the fabric. Sweatshirt fabrics come in loopback and brushed back. If you want that OMG-it-feels-so-soft-on-my-skin feeling, go for brushed.
You don’t have to use sweatshirt fabric. Other options are available, from fashion-forward neoprene (aka scuba) to a more eyebrow-rising choice like crushed velour (aka velvet).
Or if you have given up on class, you could go for fleece.