How do we keep competitors from simply copying our app?

You need to be very careful here. In the US, you have a 12-month period where you can have something on the market and then file for the patent (this is under the new revisions to the law under the America Invents Act (AIA)). However, this could prevent your ever getting a patent anywhere outside of the US.

At the very least, you should file a provisional before having a public disclosure. That gives you 12 months before you have to file a utility and presumably by then, if you're trying to conserve cash, you'll have a better idea where you stand.

Replicating the functions of software is different then replicating your IP. There are a lot of ways to bake a cookie but if you have a unique process for doing so that's patented, then I simply can't bake them your way, just any other way.

You also don't need to patent everything. You need to look at the most novel aspect of your invention. That may involve the way you move data -- or the nature of the buffering between the app and the entertainment opportunities, etc. You don't need to, nor can you, patent the app itself. Rather you can patent unique methods and any apparatus used therein.