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It is not wise to keep your Bitcoin in an exchange, because it involves a third party, and if we can remember Bitcoin was not created to have a third party system, therefore it is risky keeping your coins in an exchange, and even if it's necessary it's should be a very small quantity that if denied access will not affect you.
It is better to keep your Bitcoin in your private wallet than in an exchange, where you can have access and control of it whenever you want it.
It is problematic, also, to send many small transactions to private wallets, including that Bitcoin.com97 mentioned that he was buying $10 per week, and so how often would you suggest that he sends his transactions to a private wallet? Every week? Month? Quarter? twice a year? what? If he is consistently investing $10 per week, then that would be $40-$50 per month, around $130 per quarter., $260 per 6 months and $520 per year.