Stripe is a good option. It works with more than 100 currencies and all major credit cards. You can also integrate it into your website, which is convenient if that’s how clients originally discovered your services.
Banks usually offer their own exchange rates, which is usually a pretty hefty "hidden fee". TransferWise uses the mid-market rate and charges you for the transactions in a more transparent way.
Apple Pay is compatible only with iPhones and only those that include an NFC and Secure Element chips which currently is only iPhone 6 and iPhone 6 Plus.
Android Pay functions as a platform that allows third-party developers to create payment apps on top of it not as a standalone app itself. This potentially will enable higher competition between available frontends and as a result better solutions without having the payment information tied to one tool.
Google has a partnership with Bancorp Bank that issues a Virtual Card to Google Wallet users that works as an intermediary between customer's card and merchant. It gives more choice in terms of compatible cards and works as a card fraud mitigation technique.
You never have to give out personal information when sending or receiving payments, only an email address. So there’s never a risk of having your personal information stolen.