Battery electric is dumb, don't do that ever, unless you are gigachad enough to do it with lead-acid batteries on branch lines only. Overhead is objectively the best form of electrification, although I like the aesthetics of third rail better. Third rail can only be DC, as AC is too dangerous, but overhead wire can be DC or AC. One little detail I think should be in consideration for overhead electrification is putting the poles in between the two tracks so the scenic views don't get blocked.