For cold storage, paper wallets or hardware wallets like Ledger or Trezor.
For small amounts (hot wallet), Mycelium, Electrum, Armory or Greenaddress.
I think Bitcoin Core is pretty solid to have decent amounts too. I know some people that has been involved in Bitcoin since 2011, still uses the same Bitcoin Core (obviously updated) and encrypted so no one can send anything unless they know the pass, and they've had 0 problems. As long as you keep your computer clean seems pretty safe to me. I use cold storage tho just in case.