If you want to use apache then this is the generally recommended way of running php.
https://www.howtoforge.com/tutorial/apache-with-php-fpm-on-ubuntu-16-04/
If you want to run the newest version of php rather than be locked into the version in your OS repository I would add a ppa for php and use that instead.
https://launchpad.net/~ondrej/+archive/ubuntu/php
PHP 7.0 will reach eol in December 2018 so you have a while but you may want to run on 7.1 now and update to 7.2 when it comes out and so on.
If you don't want to bother with any of this server admin stuff take a look at Laravel forge which will do all of this for you.
You can also help automate your deployment process with Laravel Envoyer.