How can I run a set of terminal commands using one click?
Running it in an apple script is not that bad. you just have to run the entire script as root because sudo requires user interaction. if you do an apple script like this one:

do shell script "cd ~/Desktop/PopcornTV &amp;&amp; /path/to/npm install &amp;&amp; /path/to/node atv.js" with administrator privileges 


replace then/path/to/npm and /path/to/node with the output of which npm and which node

it will open up a dialogue and ask you for your password.