You wallet is your private key. There are some trusted wallets like jaxx and coinomi that I would recommend for beginners. They allow you to view your private keys in a simple UI, but there is some possibility that you could be hacked using any interface/UI wallet. You'll want to create a private/public key pair offline for maximum cold storage style security. UI wallets are good for day-to-day transactions and ease of use.
I set up a public/private key pair a while ago. The public key is: 1Bskxd3NCsQZu2pzMJPT8xaq2ve7sLFqei
so I or anyone else could send bitcoin to this address and I would just have it in cold storage until I sweep the private key with an app like coinomi at which point it would be in my "hot" coinomi wallet. Alternatively, I could trade or pass on the private key and thus transfer the coins that way. For someone to get access to the coins before then, they would have to physically take the physically printed private key. It's not possible to hack like a UI wallet would be. UI wallets also have backup phrases to restore the coins. With a cold pair, if all of the physical copies of the key are lost, the coins will be forever lost.