For WiFi connection:
Go to any Taiwan Tourist Information desk (at airport or train station or MRT station). With your passport, you can sign up for "iTaiwan". What this does is allow you to FREELY log onto any WiFi around the island that has "iTaiwan" or "iTaipei" or "iChiayi" or "TaipeiFree" or whatever. Those are free government WiFi's around the island. You'll get an id and password. Plus, when you are near a government building (like public school, or bus stop, or MRT station, or library, government bank, etc. etc.), you will see those WiFi's pop up and you can log onto the Internet for free. For a tourist, it is quite handy. If you are in Taitung, the free WiFi might read as "iTaitung" or "TaitungFree". Just have to try each one out, as each county/city has a different WiFi name, BUT you use that same ID that you just signed up with at the Tourist Info. For example, if you see "TaipeiFree", you click on it, and then type in your ID and password and click on the circle for "iTaiwan" to let them know you signed up through "iTaiwan". They are all interrelated. You can ask more about this at the Taiwan Tourist Bureau counters at those places I mentioned (airport, train stations, MRT stations).
Hope this makes sense. It's all FREE WiFi around the island (as long as you are near one of the government entities (bus stop, train station, government building, library, public school, etc.).
As for SIM cards, well, I'm guessing you'll have to see if any Chung Hwa Telecom, or Fareastone, or Taiwan Mobile is in the train station to get a SIM card