And if you are gonna sync through iCloud, you might want to go to Settings/Mail,Contacts,calendars, select your Gmail account and make sure that notes isn't set to also sync with Gmail. If it is set to sync in two different places, it can cause headaches, unless you really understand what is happening.
If you want to sync through iCloud, make sure you open your notes app and select the iCloud account, and not "on this phone"