First, before you do anything, your company must apply a work permit for you. It's their responsibility.
The application cost is TWD 500.
Then, you should pay and do your ARC application by yourself.
It costs TWD 1000 for one year extension, TWD 2000 for 2 years and TWD 3000 for 3 years.
The length of ARC extension is not your decision, but by the immigration after your company file a work permit application. My company asked for 3 years extension once, when they apply for work permit, the immigration office give them one year, so I can only apply for one year extension.
In area other than Taipei City, you have the option of them sending your ARC when it finished. You just need to pay for the mailing (TWD 26 for New Taipei City) and write your mailing address neatly (in Chinese!)