You don’t actually have to check anything on that page, since you’ve already gotten your sketch code from the forum, and aren’t using any of those options. All you need from that page is the ‘Auth Token’ in the upper right, that you can paste into the sketch in this line:
char token[] = "put your auth token here";
If everything is working correct, when you run the sketch, it should make an internet connection using that token to identify your account with our server, and the website should advance from the page you’ve pictured to a blank dashboard that looks like this:
If you need to debug, as you mentioned, it looks like @kreggly has you covered a bit farther down that thread: 
WifiShield with arduino uno compiling error - #27 by kreggly
Alternatively, if you connect your Uno with one of our supported shields (the ones pictured in your last screenshot) instead of the ESP8266 for connectivity, then you would be able to use the Arduino IDE to debug as the serial on the Uno wouldn’t be occupied with communication with the ESP.