Mycrypto is a tolerable and good wallet for me, I've used it. Trust Wallet is the wallet that supports these two coins. I would advise you better to have hardware wallets but they only support to accept Ethereum and not Zil. Based on the website of Zil, they are on Ledger but after checking the supported coins on Ledger, they are not listed. So it's one of them that's not updated.
(https://www.zilliqa.com/wallets)