Bitcoin core for full wallet. Electrum for SPV wallet.
Bet we'll see some replies recommending exchange wallets.
If you are in the Philippines, I suggest you use (CoinsPh). It is easy to use and the bitcoin is automatically converted into Peso

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Don't listen to this guy. CoinsPh is basically like coinbase. It's a fully online site, all your bitcoin is in control of them. They can run away with your funds at any time.
I don't think so, I already using it and get my pay out.