Bus from Takachiho to Kumamoto

I'm a solo traveller. I'll stay about 12 days in Kyushu, then heading to Osaka. My Kyushu trip would be :
Route 1: Hakata - Kagoshima - Miyazaki - Takachiho Gorge - Kumamoto - Beppu - Yufuin

Or
Route 2 Hakata - Yufuin - Beppu - Kumamoto - Takachiho - Miyazaki - Kagoshima - Hakata

I plan like this because I'd like to take a Kyushu-Odan-Tokkyu train ...just that.

Questions:
1. Which plan should be chosen? I'll use JR Pass 14 days.
2. Could you please recommend a budget hotel in Takachiho?
3. I can't find the bus schedule from Takachiho to Kumamoto. Normaly, people seem to take a bus from Kumamoto.

Which plan should be chosen? I'll use JR Pass 14 days.

I don't think it matters. Either way.

3. I can't find the bus schedule from Takachiho to Kumamoto. Normaly, people seem to take a bus from Kumamoto.

Here you go:
http://www.kyusanko.co.jp/sankobus/toshikan/takachiho/table/takachiho_...

熊本駅前 refers to JR Kumamoto Station
熊本交通センター refers to Kumamoto Kotsu Center in the city center
高千穂バスセンター refers to Takachiho Bus Center in central Takachiho.

You could save some money by using the bus only between Takachiho and Takamori-Chuo (高森中央) and catch the Minami-Aso Railway from there to JR Tateno Station, where the Kyushu Odan Express also stops.

Thank you, Uji.
Travelling in Kyushu could consume a lot of time, especially using public transportation. But I have no choice. Anyway, do you know Totoro Bus Stop in Oita Pref. I find that from Beppu I can take JR train to either Miemachi or Saiki and take a bus there. But I have trouble finding a bus schedule from both places, only know that it runs once or twice a day to and from Jr station.