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These Location Services options are for using the phone to access your current location, e.g., for Google Maps. I generally find that Standalone GPS is all I need: it is free, and it won't (I think) report my location to VZW or Google for their business purposes. VZW, I think, will charge for their location services; not sure about Google. Activating GPS is enough for me to use Google Maps and get my current location, driving directions, etc.
But that's not what you're looking for. What you want is an app that will locate a lost phone. Go to the Play Store (which is what Google calls its Android app store) and search for "phone locator". This will bring up a long list of apps to choose from. Most are free. Be sure to read the features and reviews before installing, to make sure you're getting what you want and that other users find that it works well. I haven't installed one of these myself (which I'll probably regret one day), so I can't make a recommendation, but hopefully others here can do so.
Welcome to the smartphone world!
