I need help with iCloud and restoring

I have an app and in order to transfer the account of the app, it says: "If you still have your old device, please sync/back up your account to either iTunes or iCloud. Next, sync your new device with either iTunes or iCloud and restore data."

I have no idea what to do with iCloud. I have my old iPhone 5 and I would like to transfer my account to my iPhone 5c. I don't have an iTunes setup for either of these devices. I just recently backed up all my pictures and videos and data into iCloud on my iPhone 5c. I have two different iCloud accounts, one for my iPhone 5 and one for my iPhone 5c. If I were to sync my old device and restore the data onto my new device, will it restore ALL the data? Will it delete any data from my old device or my new device? Can i just restore the data for one app? If possible, how?

The thing is that I dont need or want any data from my old device or than the account/data from that one app onto my new iPhone 5c.

Also, my iPhone 5c has the latest iOS. But my iPhone 5 still doesn't even have iOS 7, will this affect anything? Should I update it to iOS 7.0.3?