Recently I had a requirement to restore the phone to the factory default and copy only Contacts, Notes and Messages because of the LowMemory issues with my phone. I have faced lot of issues after the iOs 7 upgrade and LowMemory issue was one the one of the major one. It used to crash at least one or twice because of the low memory issue and it used to log in diagnostic report. (Settings->General->About->Diagnostics&Usage->Diagnostics & Usage Data). To fix that issue I restored the phone to the factory default and restored only contact, message and notes.
1. Connect to the iPhone to the iTunes
2. Click on the summary tab in the top menu and disable the menu “Automatically sync when this iPhone is connected.
3. Right click on your device name listed on the left hand side menu.
4. Click on the “Restore from the backup” option. This will list out the previous two backups. Select the backup which you wish to restore. Then this will restore only the basic data like contacts, notes and messages from the previous backup.