15 day budget travel around Taiwan

Hi
We have a group of 8 pax planing to travel to Taipei in May 09 (15 days).
The places that we intended to visit are :

1) Taipei to Shitoushan
2) Shitoushan to Sun Moon Lake
3) Sun Moon Lake to Alisan / Rueli
4) Chiayi to Hualien
5) Back to Taipei / Kee lung
6) Proceed to Jiufen

We intended to travel on Budget and would really appreciate if you could
give me some information on the best way to travel (especially from Taipei
to Shitoushan, is there any bus or train that we can take and how much it
will cost). Also appreciate if you could recommend me the hotels and the
best route to move from one place to another...

Thank you very much in advance and hope to get your reply asap.

I don't know the exact

I don't know the exact details of the bus to Shitoushan, but you will need to first go to Zhudong. Buses leave about every twenty minutes from the Intercity Bus Terminal on Chongqing Road to the west of Taipei Main Station. 

From there transfer to catch a bus to Shitoushan. The bus service to Shitoushan will not be very frequent. I advise you to call the tourist bureau hotline or check with the bus station in Taipei for further details.

Your basic itinerary seems well planned although travelling from Chiayi to Hualian is quite a long way. Maybe a stopover in Kaohsiung or Taidong could break it up a bit.