Hi Vince,
Airlines / Ticketing
Most airlines allow you to perform seat selection if you are their frequent flyer...... Soem with more advanced Internet direct purchase (Like SQ, Jetstar) allow seat confirmation on purchase of the tix. I'd suggest that you log on to the website to find out ?
So far, what I do know is that Jetstar, SIA, EVA Air and China Airlines have direct flights to/from Taipei. See of United Airlines/Northwest have stopovers there from US to Singapore. Not too sure with all the changes in the scheduling of flights from the downturn.
EVA Air is a Taiwan carrier related to the Evergreen Shipping Group. Definitely safer than C**** Airlines which has had it's share of unfortunate incidents. Yeah, the Economy Deluxe seats were even ahead of SQ's exec economy on the A340 which no longer exists....
Hotels
The one nearest is the Grand Hyatt which is right next door to the WTC and also the Taipei 101. Pretty cool to stay there but prices quite steep.
If you don't mind a short walk from the Taipei 101/WTC/Sogo area across from the Sun Yat Sen Memorial, there's a hotel called United Hotel at the corner diagonally opposite the SYS Memorial which is more reasonable. 4 star, not so much frills, but pretty good. Even have a Men's Sauna on the top floor (16th floor I think but they skip 4th and 14th so go figure) with full length glass windows WITHOUT curtains or blinds and shower points OPPOSITE the sauna. Never quite got that one figured out but.... hahaa ... Sounds exhibitionistic.
And oh, it's right about 50m from the nearest MRT entrance "Sun Yat Sen Station". Google the place and you might have some pix....