I carry my S3 in a small wallet case, one of the ones where it just snaps in and there are two places for an ID card or credit card on the other side. It's perfect for work since I keep my work ID and my debit card in it. It's also nice if you don't want to carry a purse around.
They make ones that are more like an actual clutch type wristlet that secure and hide the phone a little better (if it can't be visible), and they are pretty handy as well. They have a handful of both types for the Note 3 on Amazon if you do a search for "Galaxy Note 3 Wallet Case". Just something to look in to. I'll probably be getting something like what I have now when I get my Note 3. It will depend on how it feels in my hand I think.