Rule of thumb: forget about 'web wallets'.

I'll say it again: do not store your coins on third parties' servers. This practice goes against the core idea of a decentralized currency and puts your assets at risk.

Always store your coins on a device that you personally own and control. Your least secure option is to use a mobile wallet. There are many mobile wallet apps on the market, but I won't recommend any of them because they inherit all the security flaws of the underlying platform - be it iOS or Android.

A better option is to use a desktop wallet (assuming you're using a Unix-based operating system, i.e. Linux or macOS). Check out Exodus - it's a clean, lightweight, cross-platform wallet app that handles ETH, BTC and a bunch of other assets.

The most secure way is to use a hardware wallet such as Trezor or KeepKey.