Note that older versions of MySQL and PHP may have reached End Of Life, which means they are no longer updated and can expose your site to security vulnerabilities. For this reason, it's best to follow the recommended setup below and use the latest versions of MySQL and PHP that your host supports.
It is recommended you use a robust platform comprised of the Linux operating system, and either the Apache web-server or the NGINX web-server. Almost any server that supports PHP and MySQL will work. If your host doesn't support one of these platforms, and mod_rewrite, you will probably be better off switching to one of the many hosting providers that do offer those choices.
It is also essential that your host allows remote connections, for many of the WordPress features to work. If your host blocks outgoing HTTP connections, many parts of the WordPress will not function.
PHP 5.6 and MySQL 5.5 or greater is recommended.
Hosting is a commodity these days and with a little digging it's easy to find a host that supports the above. If you're looking for hosting suggestions, please try: