I did option 1 and don't recommend it because it is a bus. Can't tell you if it was scenic because I did the trip at night. Can tell you that it winds it's way around, bouncing along, and I was glad when it was over. The bus driver was friendly and looped back around in Hagi when I didn't get off at the right place. But no reason to take the bus if you can take the train.

I took the San-in line from Hagi to Matsue. That trip is interesting, scenic, as it goes by the Nihon Kai. Made a nice lunch stop in Masuda between train connections. It's quite rural there (along the San-in line) so you'd want to choose your trains carefully as the locals would make lots of stops (taking children to/from school for example).

I'd probably take option 2 because it is a shorter tho it would be tempting to take the San-in line the whole way around, just to see what there is to be seen. If you do take option 3, you could stop at Shimonoseki, the world capital for fugu, and have sashimi.

Hagi is an interesting place to visit. That whole region is a bit less well off than the Japan that most of the tourists see. Where are you headed after Hagi?

Looks like the via-Mine-Line option can be 60 to 90 minutes less travel time than San-in line from Shimonoseki. Option 2 already has 90 minuts on JR locals, would not want to add another 90 minutes to that.

Thanks for that information. I'm not averse to buses or slow trains if the journey is scenic.

After Hagi, I'm continuing along the coast to Izumo and Matsue (then to Takahashi) so I'll have plenty of opportunity to see the coastal scenery and I think that allows me to drop option 3.

That leaves option 1, which offers the possible advantage of dining on neurotoxins in Shimonoseki but the disadvantage of having to digest them on a jolting bus, versus option 2, which seems to have no strong positives or negatives.

Well, researching further... the Mine line goes by the Akiyoshi-do cave, "one of the largest stalactite caves of its kind in the orient", located in "the largest limestone plateau in Japan, known for its Karst topography". And Wikipedia tells me that the Burren in Ireland is an example of Karst topography, and I've seen that and it's pretty spectacular so I think I'll move option 2 to the top.

I'd appreciate any other first hand accounts.