The minimal server requirements are essentially the same as the requirements of the WordPress 4.9.x line of releases.
- PHP: version 5.2 or above.
- Database: MySQL 5.0 or above, or MariaDB (any version).
Please keep in mind that those are the minimal requirements, and they are not the recommended ones. The recommendation is to always use the latest version of the PHP and DB software, especially if you are starting a new site, as upgrading when the site is live is always a stressing experience, and you should minimize it as much as possible.