Hide glue if you want to be authentic.
Regular
wood glue if you want to be practical.
An epoxy such as
US Composites #635 if it's in really rough shape/is missing chunks of wood (if you're missing chunks of wood you'll also need a thickener such as fumed silica so you can fill these areas).
If the wood is in decent shape, I'd recommend regular wood glue and linseed oiling the crap out of it after the glue sets. Hardest part is to remove the pins they used at the finger joints without breaking anything.
If you go the epoxy route, it may be best to 'wet out' the wood with the epoxy thinned with ~10% acetone before glueing it together, this will give you a better bond and help stabilize/strengthen the old wood.
-Tyler