The bitcoin is safe but it stays a investment so keep that in mind when you are investing into it, with other things like safety its safe without any doubt so long you do not store your large amounts into online wallets.
Yes, I agree that you shouldn't let your BTC be kept by other people. Let yourself keep them. So whenever you have a finish transaction with an exchange or website, better to withdraw all your coins to your own wallet for safety measure. With this, you don't have to worry about sudden closing of exchanges because of bankruptcy.