The train to Kushimoto: a JR West 283-series Kuroshio express. The sets are getting on a bit, they were introduced in 1996 and the livery could do with a refresh, but the "dolphin nose" is distinctive, and I, for one, really like it. They're also quite rare, only 4 sets exist.
The Kisei Main Line is essentially the coastal route from Nagoya to Wakayama. The full trip around the Kii peninsula takes 8 hours by express train, with a change required at Shingû or Katsuura, but it's definitely scenic as it gets very close to the sea (photo between Kii-Tahara and Koza).