In a dual monitor system, when starting a Windows 8.1 Store app from the Start Screen or the desktop Task Bar, an app will display its main page on the same monitor that it has been launched from.
I am looking for a way to start the app display on a specific monitor i.e. the primary monitor.
Unfortunately, as of Windows 8.1 there isn't an option to control this. If you have a specific scenario in mind, the best thing to do is describe the need via a request on wpdev.uservoice.com.
Generally speaking, Store apps get only limited information about monitors and system configurations, e.g. I don't know of an API that tells you what monitor you're on.
It's possible that there are third-party configuration tools that let you control this sort of thing, like the ones that let you run Store apps in a desktop window. I don't have any suggestions, however.