The security considerations for choosing a Stellar Wallet is same as the ones you consider when storing other crypto assets.
- Make sure you install an open source client/wallet whose code is audited and maintained by community members.
- You can also install the wallets developed by their respective creators/foundations/companies.
- The strongest wallets are multi-sig ones. This means you need multiple keys to authorize a transaction occurring from that wallet.
- Does the wallet allow you to do a backup? If so what are the available options for backup? Because if your PC/mobile is stolen or damaged, without a backup available you would lose all access to them.
However all of the above are software wallets. If you are holding any assets which is equivalent to the price of 10 cups of coffee, I would strongly advise you to go for the hardware wallet. Hardware wallets physically insulate your address/wallets from the web or any system as such and can generate multiple addresses and keys. Moreover you can store multiple types of currencies on them.
The current option for hardware wallets is the Ledger Nano.