Neither Coinbase nor Xapo are wallets per se.  They're online wallets, which are basically a bank that you're trusting to store and spend your Bitcoin for you.  A proper Bitcoin wallet is one where you control your private keys - these are wallets like Electrum which you download.

You can also deal with hardware wallets like a TREZOR, and use these with Electrum if you want.  I would argue that these are a very safe option for users who are not tech-savvy.

Alternatively you could use Bitcoin Core, which is a full node.  This way you're contributing to the security of the whole network.  However, it can be resource intensive to run these clients.