The right sweatbands can make your workout better because you won't be constantly wiping your face on a towel or on your sleeve. You can wear an ordinary bandanna as a sweatband, which fits well under mesh running caps. As a veteran long-haired runner, my sweatband style is to put my hair in a ponytail, braid the ponytail, wrap a bandanna around my head and tie the ends around the ponytail, and top it off with a mesh baseball cap that has a Velcro closure and a hole for the braid to fit through. The hat doesn't slide around, and I wear it this way for training and for marathons (and even for a 50-kilometer run).
But if you are workout out indoors and not wearing a hat, choose a sweatband made of terry cloth or moisture-wicking fabric because they will be more absorbent.
If you just want to keep layers of hair off your face, try a narrow rubber headband. These trendy bands were popular among the women athletes in recent Olympics, and you can find them at most places where sports apparel accessories are sold.