You need to use wallet which gives full control of your BTC. On exchanges you don't have control of your coins. Exchanges aren't designed to be wallets, they only gives deposit addresses for every account. If exchange will turn into scam, bankrupt or will be hacked you will lose all money that you had on exchange. Don't use exchange as your wallet, keep money only that you need for a trading on exchange.
And I don't recommend to use online wallets. It would be best to buy hardware wallet or make paper wallet. Electrum desktop wallet can be a good option, but you must be careful to avoid malware which can steal your BTC. Shortly, read sticked topic on bitcointalk and before using wallet read tips how touse that wallet properly and secure your BTC.