What coding language to use?

This is obviously a special setup. I would approach it as follows:

1. Create a plugin that allows you to create a special page template. This special page template will house your interactive page. The reason for creating a plugin is to ensure that special page is independent from your theme. So if you decide to change your theme in future, this page would still work. But also, make sure that the formatting of this page is somehow standardised across all themes to make it more universal. The content of the page you are creating could be a shortcode.

2. When you create your special page, create the page using this template you just created.

3. Back to your template, use any language you like that you are comfortable with, and that fits your needs. However, I am inclined to use PHP and JavaScript (and JavaScript libraries, such as jQuery, and other libraries) because this is the basis of WordPress and is easier to handle.

Hope this helps