For building a web application you have many choices: NodeJS, PHP, Ruby on Rails, Python, Java, C#, etc. As long as it can be used as a web server or run an embedded browser to display the battle.net login page you can use it.
You can check a list of community libraries so you don’t have to write everything from scratch.
All of them (plus some others I didn’t mention) can achieve the same result in a different way.
This is just my own opinion, but I think NodeJS and PHP are easier to learn. They are a good starting point. The one I prefer and enjoy coding is Ruby.