I've had luck with Pagodabox as a PaaS. Easy deploy, easy to add extensions, change PHP versions, etc. SSL certs are a breeze with them as well.
Here's an example of a Boxfile for a Cake app, their version of a build + deploy recipe. As you can see, it uses PHP 5.6, however upgrading to 7.0 is as simple as changing those version requirements and pushing. It uses a network storage component for file and image caching, a redis instance for other caching, and a mysql database. It also installs a few different extensions for image manipulation and such.
Adding deploy hooks is really easy as well, and you'll see I run migrations and clear cache, though you can do much more. I suggest checking out their docs, they're very nice. They also have excellent support and you can even jump in IRC for quick issues.
- "composer install --no-interaction --prefer-source"
- "bin/cake migrations migrate"
- "bin/cake orm_cache clear"