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I personally run or manage websites run on Bluehost VPS, Siteground, and iPage. This WordPress blog is hosted by Bluehost VPS. Just for your reference, Siteground supports PHP 7.0, PHP 7.1 and even PHP 7.2 RC.
If you want a cheaper webhosting service, iPage will be a good choice. I prefer Siteground; I think it's speedy and stable.