Building web app

I want to create a web app, and therefore done some research. Notice that it is a web app, and not a native app, as users shouldn't need to download the app to their phones.

There are a lot of frameworks for this (way too many). My choice ended on JQuery Mobile, which is a JS, CSS , HTML5 framework (among many others).

My question though (and concern), is how to integrate the backend part. I will need more than just a static site. At some point, I will need to store user information, which requires a database (and backend language. I prefer Java or C#).

In my search for web app frameworks, they all discuss the frontend part, and none (that I found anyway) emphasize the backend part.

So let's assume that I have created a web app using JQuery Mobile, or any other framework that uses CSS, JS and HTML5. Now as an example, I want to store contact info from the user (via contact formular or so). I will need to process this info, and store it in a database (MySQL or SQL). The processing will happen in code behind (Java/C#). But this code will need to be compiled, which leads us to the need for a framework that can handle this (if such exists).

Is there a framework that can help me do this (Like Visual studio does, when creating sites in .NET)? And can you point me to any resource that can help me out/explain how to, if I am forced to compile everything by hand?

Thanks

I am developing on Ubuntu.

Short recap.

If you are confused after reading the above, shortly... Developing a web app using JS, CSS and HTML5. How do I integrate the backend code?

Ps. I stumbled over PhoneGap, but from what I see, it only used to create native apps?