The Express products are completely functional although they lack certain non essential features. The main limitation of the Express editions is that you can't use third party plugins with them. Third party plugins are used to enhance Visual Studio itself and are not to be confused with third party libraries which you can download conventionally or with the built in package manager Nuget.
The Express editions are distributed by task so you only download what you need. If you don't want to create Windows Phone apps, for example, you don't have to download that functionality.
To develop web apps you have to download Visual Studio Express 2012 for Web.
http://www.microsoft.com/visualstudio/eng/products/visual-st...
It allows you to develop ASP.NET MVC and ASP.NET WebForms apps with C# or VB.NET right out of the box but you can also use it to develop web services with WebAPI, regular HTML5 websites, etc. And out of the box you can deploy by using FTP, WebDeploy and Azure but you can also use whatever external tool that you like.
The product includes a copy of MS SQL Express that runs as a process but you're not limited to using Microsoft databases.