Which wallet is best to transfer purchased Bitcoins to?

I want to transfer purchased Bitcoins from the exchange to my wallet. Which wallet is best to choose: Trust Wallet, Atomic Wallet, Jaxx Liberty, Exodus? Are any of these wallets linked to an exchange, and if the exchange goes down, will the funds in that wallet be lost as well? Is it better to install a wallet on a smartphone that is used and online all the time, or is it safer to install it on an old, unused smartphone that may be lying around and offline? Or maybe it's better not to bother with such wallets in the form of applications and spend money on buying a hardware Ledger wallet?