I assume most of us keep our coins in some hardware wallet (usually Trezor or Ledger). This is one of the safer ways. A software wallet from a good source will suffice for smaller amounts (if a hardware wallet is not currently an option). Be sure to download only from official sources and learn how to verify signatures. If you plan to trade regularly or take advantage of some of the additional benefits given by the exchange, you will need to keep your coins in their wallet.

You know, you can move your coins from one wallet to another at any time? So any choice that you take doesn't have to be final.
For example, I have some of my coins in the exchange, some in the casino where I gamble, and a larger part on a hardware wallet that is used for long-term storage.