After purchasing any coins/tokens withdraw them to your personal (desktop-/hardware-) wallet.
The safest option to store your coins would be a paper wallet. Its the best option for storing long term and when you don't access your funds often.
A hardware wallet is not much less secure than a paper wallet. It combines the positive effects of having an offline storage with the benefits of being able to spend the funds easily.
The downsides of hardware wallets are their price (50$+).
Webwallets / Keeping coins at exchanges are the worst option to choose from.
Cryptocurrencies are invented to be a trustless system. When you trust an exchange/web wallet to store your coins your destroying the sense of crypto and the reason it is made for.
Just additional negative factors, no real benefits.