mvc_3

Now, I would like some suggestions on what or what kind of application I create to practice?

You can build anytype of website. Stackoverlow is a great example of a high traffice site. Parts of Woot.com is built using asp.net mvc. Kelly Blue Book has features in asp.net mvc. These are 3 very different sites , but you can really build any type of website.

In addition with mvc 4 you can easily build sites that work on both desktop and mobile devices. ASP.NET vmc also makes it very easy to build single page applications that are javascript heavy.

I would recommend you start with a simple website to manage tasks (like a todo list). Then go back and modify it to render differently on mobile devices and lastly incorporate some single page application features.