Your Alien Residence Certificate (ARC) is your main form of identification in Taiwan. The IAA front office staff will provide you with all the information and documentation you need, and then you'll head down to the immigration office near Xiaonanmen MRT station (Green line). Take a look at the IAA internal site page for more details (requires IAA username and password). If you have any questions though, feel free to ask for help from your fellow postdocs.
You will need a current passport photograph to get the ARC; there are photobooths in the basement of the immigration centre if you forgot to bring one with you.
When you get your ARC you can have it validated for use with the e-gates when leaving/entering Taiwan. There is a stall near the entrance to the immigration centre (left hand side as you face the service area at the rear) where the staff will take your ARC and activate it for use with the e-gates. The service is free of charge. This means you can skip the queue at immigration, swipe your ARC, and be on your way to departure much more quickly. If you get a new ARC you need to revalidate it for use with the e-gates, but do not need to revalidate it after renewal.
When getting your ARC you can pay 1,000 NTD per year; since the ARC is tied to your employment in Taiwan you can thus pay for two year's worth of ARC up front, which saves you the trip to renew it every year during your time in Taiwan.
You might want to wait until you find an apartment before getting your ARC, otherwise you will have to make a second trip to the immigration office to update your address.