Most of the ones I have worked on were made of oak. A few were southern yellow pine, but they were produced when old growth timber was still available. The threshold will be one piece, so you will need to get something just as wide and thick or do a glue-up to match. The door jambs are rabbeted to accept the threshold and nailed in from the side of the jamb. You could replace it without removing the entire jamb but will need to shim under the new one to keep it tight to the top of the rabbets.
If its not too rotted you might want to consider and exterior grade wood filler and repaint it. Good luck with the project.
