Bitcoin, desktop
Sparrow Wallet. Privacy-aware, coin control, PSBT, hardware wallet integration. Best default.
Electrum. Lightweight, reliable, less privacy focus. Fine for basic needs.
Monero, desktop
Feather Wallet. Lightweight, no full node needed, actively maintained. Current default.
Monero GUI. Reference wallet from the Monero core team. Requires either a full node or a remote node. Best privacy for readers running their own infrastructure.
Monero, mobile
Cake Wallet. Mobile-friendly. Built-in Bitcoin-to-Monero swap through integrated providers. Good default for readers who use their phone.
Hardware wallets
Trezor and Ledger both work for Bitcoin. Trezor has better Monero support of the two.
Hardware wallets protect your private keys from software compromise on your host operating system. Worth the cost if you hold coin for extended periods. Not worth the friction for coin you plan to spend within a week.
What to avoid
Custodial exchange wallets. Browser extensions like MetaMask. Mobile-only Bitcoin apps that do not publish the private key.
Any wallet that requires an email address at setup. Any wallet that syncs to a cloud account by default. Any wallet that does not let you export the seed phrase.