Set up your first Bitcoin wallet. If you don't feel technically competent, it's perfectly acceptable to ignore the next few steps and just leave your bitcoin in the account where you bought them. In fact, most bitcoin holders do just that. But the beauty of bitcoin is that it's money that no third party needs to control for you. In addition, since exchanges store hundreds of millions of dollars of bitcoin, they are a very attractive target for hackers. So unlike stuffing dollars in your mattress, it's actually safer to store your bitcoins on your own rather than trusting them to an exchange. All the wallets listed here will not give any third-party access to your bitcoins:
Mobile Wallets are Bitcoin wallets that run on your mobile device. Such wallets are portable and practical for in-store use. Mobile devices tend to be less prone to malicious software than are computers, creating a reasonably secure environment for small amount of bitcoin. Some of the best mobile wallets are:
Airbitz
Mycelium
BitPay
Jaxx
Web wallets are convenient and user-friendly, because they are always available online. All you need to do is set up an account and log in. The most popular web wallet is:
Blockchain.info
Hardware wallets are highly secure and mostly foolproof. If you are new to bitcoin and want to store a lot of bitcoin safely, you'd be smart to invest in a hardware wallet. Popular hardware wallets include:
Trezor
Ledger
Paper wallets are very secure for long term storage. While paper wallets are highly hacker resistant, they are cumbersome when it comes time to spend your bitcoins.
Learn how to create and use a bitcoin paper wallet here
Advanced wallets are not a great starting place for beginners. This is the type of wallet for which Bitcoin was originally conceived. You'll have to run a local copy of the blockchain to keep your transactions anonymous. The better known software wallets include:
Armory
Multibit