Does anybody have the telephone contact for the cheap 700NT taxi shuttles?
Try the Airbus service. It is only 100NT and picks up and drops off at a lot of the big hotels here in Taipei. Their number is 0800-088-626
They run from 4:40am to really really late, and run every 20 minutes. Nice too! I would suggest giving yourself an hour and a half though to get there.
If you already have an English teaching job lined up then make sure you have someone from the school meet you at the airport. I think most schools will do that for newly arriving teachers. Have you asked your school to send someone to meet you?
Choosing which bus company to take into Taipei can be a bit confusing since they each have different routes and stop at odd places. In addition, when the bus company says they will stop at some place that means they will stop on the street somewhere NEAR the supposed stop. For example, the FreeGo bus says it will stop AT the Westin Hotel but actually stops across the street from it, which makes it a pain for travellers with several heavy bags.
Ticket prices are about the same for the 3 bus companies - around NT$110 ~ NT$130 per person.
For a first timer to Taiwan, I suggest taking Airbus because that makes stops all over Taipei near the major tourist hotels. There are two routes to choose from.
If that is all too confusing to take a bus to Taipei and then a taxi to your hotel/hostel then just take a taxi direct from the airport for NT$1000+.
For taxis here, definitely have the address clearly written in Chinese. An english only address will be useless.
Good luck. Remember to take your anti-culture shock pills religiously for the first year you are here.