Writers use many note-taking applications on their iOS devices. Some of them are very advanced, like Evernote, but frankly, how often do you tag notes, mark them as favourite or print?
If you want to have a quick way to write something down (quick = minimal number of taps) and you want your notes to be synced between iPhone, iPad and a computer, the simplest possible way is a default Notes application. There is no reason to spend extra money on an advanced note-taking app, if you only want your notes to be accessed from a computer.
Syncing is handled via Gmail. If you added your Gmail account in the Settings » Mail, Contacts, Calendars make sure notes are synced [picture 1].
If not, turn them on. Since that time all your notes will not only be synced between iOS devices, but also a special tab, called Notes, will be automatically created in your Gmail account.
What you have to remember is that it’s good to wait a couple of seconds before closing the app to give it a chance to send the new content to server [picture 2], but this is applying to all apps with sync functionality.