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Whatever your currencies or tokens, do not do it:

Leave your crypto-currencies on an exchange. When a theft of crypto-currencies occurs, it is mainly by attacks on the exchanges.
Yes, the exchanges all offer wallets, but they should only be used temporarily. The service has access to both your public key AND your private key.
The same problem occurs if you use Web-wallet: You must trust a third party about the security of your private key.

Security level 1 = wallet software:

Use a wallet software on your smartphone or computer. Here's a comparison of the security and anonymity levels of the most popular apps and software: Bitcoin Wallets Comparison
Here, the major improvement comes from the fact that only you keep access to your private key. So, we must be careful not to lose this key and ensure that it is not readable in case of theft of the computer or smartphone.

Security level 2 = hardware wallet:

Aside from the Paper Wallet's not very practical solution of printing these public and private keys on sheets of paper to recapture each transaction, there are very good Hardware Wallet, both safe and practical:

The famous Ledger Nano S (99 €) that looks like a USB key. Since the key is not permanently connected to the internet, it is particularly secure. Ideal if you can not afford to lose your crypto-currencies. And it's French sir.

The Trezor One (€ 85) or Model T (€ 180) are not bad either but are a little less popular.