I'm currently planning my Taiwan itinerary as well so I can answer some of the questions. I am using Route A for my trip.

From Taipei To Sun Moon Lake, you can take HSR to Taichung station. From Taichung, you can board a bus. Perhaps you can get more info about the buses here: http://www.ntbus.com.tw/033.htm or http://www.rybus.com.tw/travel_lines_135.html. From Taichung HSR -> SML, it might take 1.5 - 2 hours to get there via bus.

From SML->Cingjing, if i remember correctly, you'll need to take a bus from SML to Puli. From there you transfer to another bus from Puli->Cingjing. Should take atleast  1.5 hours depending on how long you need to wait for the bus transfer at Puli.

For my case, I'm making a day trip to Sun Moon Lake and then head to Cingjing. I've booked a driver for this.

For the route from Cingjing to Tarako, I think the best way is to book a driver. I've booked a driver, Mr Li 0937980512 (teming_li@yahoo.com.tw) from Cingjing to Taroko. 

I was also deciding if i wanted to go from Taroko to Cingjing. But i decided not to since it'd take about 2.5 hours to get to Hualien from Taipei via train , about 5 hours around Taroko and then perhaps 4 hours drive to Cingjing. Our driver mentioned the route between Taroko and Cingjing is quite dangerous especially so when it gets darker.

For Cingjing, I am staying 2 nights. First night at Starry Minsu (http://starry.nantou.com.tw/l) and second night at Shangrila Hanging Garden Resort (http://shangrila-resort.hotel.com.tw/eng/). Starry Minsu for the top down view of Cingjing town and being closer to the stars (tho i heard people complain about the dangerous & narrow road to get there).  Shangrila Hanging Garden Resort  because its inside the town and for a different environment.