One thing you always hear is that you should not store your coins on exchanges and that you risk losing them in a hack.
Obviously, Why you want to trust someone whom you don't even know and you know that many exchanges ran with peoples money. That is why everyone asks you to keep your bitcoins in your online web wallet or in offline wallet.
When you buy your bitcoins you should immediately send your bitcoins to your wallet so you have some security over your coins.
I often use blockchain.info since they have released its beta version they have added many security measures in it. I must say that you should use and signup. They are online from many years and very trusted, I never had any problem with them.
But if you are looking to store them offline, Use something portable, but do not lose your portable device. Offline wallets are the most safest one.
Good luck! With your selection.
Please use this link to know more about wallets and select the best of em.
Again, I am not talking about Bitcoins.
And why would an online web wallet be less prone to people taking the money and running? What exactly makes an online wallet safer vs regular exchange? No one has explained this. And what exchanges that have had any traffic has been one of these take money and run sites? I have never heard of this.