you can't/shouldn't add the App_Code folder to a Web Application because this folder is designed for runtime compilation by asp.net and the Web Application project is designed for you to precompile your website into a dll which you can find in the Bin folder and deploy to your site. If you do add this manually, you may end up getting name clashes as the class will be precompiled to the dll and then asp.net will again try to recompile at runtime.
So, for Web App Projects, you should instead Add a folder called something like 'CodeFolder' and then add you class in there. Then right click properties on that class file and set its build config to compile rather than content.
I am working on my own web project for www.athenatennis.com.sg and am going thru a similar learning curve with that.