Cryptocurrency coins and tokens are digital, and once you bought them, the next problem is where do you store them.
I wouldn't recommend this, as exchanges are not dedicated crypto wallet or safekeeping systems. In fact, there is a specific event referred to the "Mt Gox" (an exchange) which shut down and investors lost a lot of bitcoins.
My Ether Wallet (MEW)
Ethereum coins and tokens can be stored in your My Ether Wallet (MEW) - it's free to download and use.
Special Cryptocurrency-Specific Digital Wallets
Certain cryptocurrency may have their own digital wallets, which can be stored on desktops or even in private serversSpecial Hard/Physical/Offline Wallets
Trezor, Nano and Ledger
This is done by printing all your private keys of your wallets, exchanges, everything into hard copy paper, stored in safe. With at least 2-3 copies.