My answer sounds like a product pitch but it's not intend as such other than "it actually works".
We use a T-Mobile plan in the US which comes with free data and texting in 100+ countries and is competitively priced. No need for the ridiculous fees that Verzion, AT&T etc charge for international service (which is typically something crazy like $10/day).
We've used it in over 30 countries so far and never had an issue. It's on the slow side, but coverage is good and it's certainly fast enough for authorization, Google Maps and WhatsApp.
Phone works immediately when you enter a new country. You don't have to do anything and there is no need for a SIM card or a local phone number.