Recommend that you back it up in iTunes rather than iCloud. Even if you are backing up to iCloud you can still perform a manual backup in iTunes by connecting your phone, right-clicking on the name of your phone on the left side and selecting Back Up. When you set up your new phone, when given the option, you'll want to choose Restore from iTunes Backup. (Also, restoring to an iTunes backup is often much faster than restoring to an iCloud backup.)
As a precaution, I recommend that you also sync your old phone with iTunes to transfer all your purchases to your iTunes library, import your photos and videos to your computer (http://support.apple.com/kb/HT4083), and be sure to back up your contacts separately (such as by syncing them with iCloud or using an app like My Contacts Backup). I say this because many users seem to report that their contacts and photos are missing after they restore from their backup; this way you're covered.
If you have problems backing up your new phone to iCloud, try deleting your last backup (if you have one) and try again. If that fails, you may have an app that is preventing the backup from succeeding. To locate which one, go to Settings>iCloud>Storage & Backup>Manage Storage, tap the name of your device under Backups, then turn a number of your apps to Off under Backup Options (tap See all Apps to view them all) and try backing up again. If it succeeds, turn some more apps On then try again; repeat this process until it fails. Eventually you'll be able to locate the offending app and exclude it from your backup if that's the problem. There are additional troubleshooting steps for iCloud backups here: http://support.apple.com/kb/TS3992.