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Hacks on exchanges are rare, but they will happen again. Freezing of exchange-accounts can happen. The point of bitcoin is to be your own bank, a bank that no one can shut-down. The only way to be your own bank is to control your bitcoins yourself.
Popular mobile wallets (great for beginners) include: Breadwallet for IOS, Mycelium for Android. Also, if your phone is rooted, please research how this affects security on mobile devices. Note: losing your phone will not lose your bitcoins if you back-up your private key seed that these apps provide you.
Hardware wallets (gold-standard of security after a bit of research) include: Ledger, Trezor, and Keepkey.
COUNTERPOINT: This post is meant to WARN newbies of a risk they might not have considered. Keeping your BTC in an exchange can be a completely valid choice – but you need to know the risks and do the research yourself. Exchanges are not banks – they are not insured by the FDIC in case of theft. If your exchange is hacked you're out of luck. People are still waiting for the Mt.Gox lawsuit to see their lost coins.
To be your own bank, you also need to trust yourself. If you get a wallet, but forget the private key or "seed" – your bitcoins are gone. The bottom line is: if you don't understand bitcoins, please do your research on proper storage. If you determine that you'd rather run with the risk of an exchange hack, at least you will be informed.