I recently did this in Hualian, went with my relative (who's Hukou I was listing under) and brought with me my Taiwan passport w entry stamp and a couple of passport photos (I'd recommend getting these done in a Taiwanese photo shop and let them know it is for your ID because the face dimensions on the photo is slightly larger than normal passport photos).
I can't remember how much the fee was but the process was pretty straight forward and they issue your ID on the spot (you may have to wait a tiny bit while they print but that's about it). Once you are listed, it is a good idea to get an official copy of the Hukou document for yourself cause you may need it for other admin purposes...
Oh! And, go get a stamp cut, you won't need it for your ID but you may as well get it "authenticated" while your at the office if you need it. Otherwise you'll need a stamp to open a bank acc anyway but I don't think it needs to be authenticated first?
And lastly, if you are not going to be employed straight away and/or want to go on the national health ins before you do you will have to register at the local NHI to your Hukou so if you are listing your Hukou in KS you may want to consider dealing w your health insurance while you are down there. If you're not in a hurry for health ins then you can always wait til your employed and your employer will sort that out for you.
Hope that helps