The one you want to keep private is the private key in the public private key pair. It's not something you can come by by accident). you wallet secures it by default. if you don't have the private key stored in a wallet or saves off line you won't have assess to the finds.
A receive address or public key starts with a 1 (sometimes a 3) and is between 26-35 alphanumeric characters. All addresses have a valid test string so generally you can't sent to an invalid address.
you can cut an past the address in the search bar on https://blockchain.info/ to see what is happening with that address.