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I'll be honest with you. Coins are only really yours when you have stored them in your personal wallet, exchanges can come and go. A good example is the current situation with Steem and Poloniex exchange, those with Steem on Poloniex can neither withdraw nor deposit it at the moment which is really devastating.

I understand... Do you know of any good personal bitcoin wallets? The amounts I am buying is so small that at the moment that I dont think the transfer fees will make it worth it.

In your case you could stick to the luno wallet for now. When you require a wallet for bitcoin, you may consider blockchain.info

Thank you very much for you insite

You're welcome