Atomic Wallet - This wallet is quite easy to use, being user-friendly and even beginners can use this easily. Atomic is an online wallet that is operable on both mobile and desktop as well.
Guarda - When it comes to online wallets, Guarda is one of the most reliable multi-currency crypto wallet. This wallet provides privacy too, as it does not store private keys, or wallet information, or even user's personal data.
The official wallets of NEM are NEM NanoWallet, NEM Mobile wallet, etc.
There might be many online wallets and many of them might be safe, but the safest option is always a hardware wallet, no matter what. It's important to remember this because if your coins aren't safe, then there's no point in investing and/or trading, as once your coins are gone, there's no way to retrieve them back. Ever!
Trezor - This hardware wallet supports 1000+ coins and tokens. Trezor is one of the most trusted wallet, is portable and can definitely keep your cryptos safe.