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.

I'll answer what I know from my research for my coming trip. Most people take Route A.
Depends on your budget and number of people, private guided tour is recommended for Cinjing and Taroko. The public transport will consume a lot of your time.
You can take the train from Hualien station to Taipei (2h plus), there's no HSR.

What's your budget for accommodation?
Do you read Chinese? It's easier for you to research. 

Early Sep is still summer holiday. I'm travelling early October.

For the first night, you could stay at

(a) SML - peaceful and quiet, not much to do in the night. Lake view wise, depends on personal preference. I don't think you can see anything in the night. You could always walk to the pier. Stay at 水社 if you want to take the bus next morning.

(b) Puli - if you are just planning to SML only and not SML + Cultural Village, then you should have enough time for SML (assuming you are taking HSR from Taipei to Taichung early in the morning). Then, you could head to Puli in the evening.

Still, you need to consider whether it's weekend or not as Nantou Bus have different schedule for Sat/Sun and Mon - Fri.

PS. There's a popular Chinese forum in M'sia. They have a lot of threads on Taiwan and some Taiwan drivers do post there, you could ask about the price.

Hey there.

I found 觀星園 Starry House's website here:-
http://starry.nantou.com.tw/?ptype=hotel

But the prices quoted in that website  are abit outdated and when i emailed him, he gave me a higher price. BTW i emailed to him in English but he replied me in Chinese

Here's the weekday room price that  Starry Minsu 李大哥 quoted me:-
6 persons room = NT$3840 per night
2 persons room = NT$1980 per night

Price above includes breakfast and Western style steamboat dinner.
I think most likely just around 清境农场 Cingjing farm, see sheep and walk around. I'm not really sure what else to in CJ do so will ask the Starry Minsu boss to recommend us when we reach there. Oh ya, if you got time , you can check out Lushan Hotspring. But i heard it's currently under going renovations. You can ask the Starry Minsu boss to find you a driver to get to Lushan Hotspring or you can board a bus yourself. If you hire a driver to Lushan Hotspring, i understand it might cost NT$650 per person which includes hot spring usage, return trip.

There are 6 of us, so our CingJing to Taroko driver asked for Nt$6000 (5-6 persons). If up to 4 persons, it's NT$5000.  Pay additional NT$500 to include Qingshui Clif, which we should be covering as well. Our driver wont be sending us to Taipei after Taroko. The plan is to board the railway train to Taipei from Hualien. Train fare should be NT$284 to NT$441 per ticket per way, depending on the type of train, date and time. http://railway.hinet.net/etkind1.htm

i'm going end sept. gonna stay a nite in Jiufen. here are 3 homestays i found quite recommended. i've booked Sunny Room. Windsor also not bad but abit pricey.

Windsor B&B http://windsor.idv.tw/WindsorD.asp
Sunny Room http://www.sunnyroom.tw/room.php
Aegean Sea http://www.aegeansea-i.com/

GMT+8 which is same time zone with MALAYSIA.

Experience to share
(1) One package is SIM card with their GSM phone, the other one is without SIM card. Both SIM card also preloaded with NTD$100 but I tell honestly the credit very fast running out as their prepaid phone charge is expensive. NT$100 can use to call back Malaysia whenever reach there (Taiwan) or call any Taxi service, Hotel or any emergency etcs services.

(2) Usually they will request you to leave your driving license or IC. I think is better to left driving license if you are not driving in Taiwan. They will return you.

(3) Terminal 1 & Terminal 2 got the counter to take/return Digital Tour Buddy. If you are taking AirAsia, then is easy as the arrival and departure should be the same terminal. I cannot remember which terminal liao but I am sure both terminal got tourism counter for you to collect/return Digital Tour Buddy.

Enjoy your trip there.

haha..do realize that tw food cant satisfy msian appetite. =P just thought there will be at least some worth trying.