I don't like going by cab because you never know when you are going to get stuck in traffic -- which has happened to me on more than one occasion. The best combination of speed and convenience for me is going by HSR.
MRT to Taipei Main Station: 20 NT; HSR to Taoyuan: 175 NT; Bus to airport: 15 NT
I'm waiting to see what the travel is like on the MRT line -- the thought of all those stops doesn't exactly thrill me. I like smooth and speedy. If the MT doesn't provide enough of a speed/convenience factor, I might still stick with the HSR.