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For Ethereum or any Ethereum contract, My Etherwallet is the way to go. Otherwise, I use paper wallets or hardware wallet (if you have the money) (think Trezor or Keepkey)

Trezor works great with My Etherwallet too. I use a Ledger and Trezor, but like the Trezor a little better, but the Ledger can hold your Alt's.

Coinomi works pretty well, is free, and supports quite a few alt coins.