With iCloud, you can back up your iPhone/iPad/iPod Touch each night, just by locking it and charging—no fuss, no having to remember to keep your Mac or PC on, etc. 

With iTunes, you can use the new automatic Wi-Fi sync, although your PC or Mac will have to be powered on for it to work. And syncing with iTunes over a wired connection must happen manually, of course.

That said, an iTunes backup is local—meaning it’s sitting right there on your hard drive, and you don’t have to worry about iCloud outages (which are inevitable).

Then again, if anything happens to your computer—like a hard drive failure (also inevitable), a flood, a fire … you’re out of luck (unless you’ve been diligently backing up your hard drive).

In other words, there are advantages and disadvantages to each. You just need to pick the one that’s right for you.

Hmmm. I wonder if iCloud’s having trouble reconciling your first backup with your next one. This is just a wild guess, but you could try deleting the iCloud backup and starting from scratch. (Tap Settings, iCloud, Storage & Backup, Manage Storage, tap the name of your phone, the press the Delete Backup button.)

BUT … I highly recommend doing an old-fashioned iTunes sync FIRST, with your sync cable, just in case. 

And if that doesn’t work, might be time for tech support.

Good luck!