If it was a simple, non-architect-designed house, it would be a native softwood, hard georgia pine or cypress. If more upscale, an assortment of hardwoods could have been specified; quartersawn oak was the favorite of arts &crafts decorators. Cherry, gumwood, ash, mahogany (or a variety of woods stained blood-red to emulate it, such as birch, maple, etc).
Casey

We had a lot of birch in our 1906 Arts and Crafts home. Also, maple for the floors was common. When installing new, spend a little extra to get taller/wider moldings. It will more closely replicate the era than the thin stuff you see today.