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.
No tienes que usar tela de sudadera. Hay otras opciones disponibles, desde neopreno de moda (aka scuba) hasta una opción más llamativa como velour triturado (aka terciopelo).