Which RDMS is best for use?

There are many popular RDBMS like MSSQL, MySQL, PostegreSQL, Oracle etc. Based on your environment and technology stack chosen you shall use one of them. For example for Windows bases systems MS SQL is recommended, similarly for PHP based technology stack MySQL is preferred. For large systems with huge transactional volume Oracle is more stable.

If you mean cloud based DB service then you can go for providers like AWS, Azure etc. They have predefined VMs available with databases installed in them (IAAS) and Azure even have PAAS too (SQL Azure database)