Can you just continue the siding (or whatever) from the underside of the eaves into the porch area?

Nice shorts.

I'd continue whatever is already under the eaves (unless it's just vinyl soffit panels). Bead board won't go with the style, so V-groove like the soffits is probably your best bet (I'm assuming plain flat is not something you're looking for).

Ha, my dad and his swimming trunks.

Yeah plain flat is not what I’m looking for. Just wanted something interesting. We purchased a light already for the entry also. Not sure why I’m fixated on a tongue and groove wood option.

I would go with beadboard or tongue/groove painted a clean white. It will be fresh and clean.