Though this is a very good and common question, what is the best blogging site where a person can make money, but it would be very difficult to answer this question in a way that may benefit the seeker in true spirit. It is because none of the platforms could earn you money until and unless you put some quality content on your site. Instead, if this question would have been asked "How money can be made through a site (platform).
However, there are plenty of platforms (both paid and free open source) which can be used to build a site that enables you to make money. All of these platforms have their own pros and cones. It purely depends on your requirements that what type of website you want to create.
The following are some of the most popular sites or platforms that can be used to build a good website and earn money.
  • Wordpress
  • Wix
  • Joomla
  • Drupal
  • Medium
  • Squarespace
  • Weebly
  • Typepad
  • Blogger
  • Tumbler
  • Ghost
All of the above mentioned are rich in features when it comes to making a website for making money. In addition to this, some of the platforms have great free and paid plugins which can be used to enhance the functionality of your website.