Blogging is big business. There are people out there who are providing services and add-on's (at a price) who will advise you to move straight to Wordpress before even passing go.
The reason that they do this is that without doubt it is the most flexible, comprehensive and expandable blogging platform out there. But... There are more setup costs... the running costs are higher... backups and technical support is essential because Wordpress blogs do get hacked and the website won't work without repair.
So to the question what is the best blogging platform. The straight answer is Wordpress. But the accurate answer is... It depends entirely on the purpose of your blog as to the best platform to choose.
Notice the heading. What is right for you? ... not... what is right for the person advising you?
Let's have a look at a few different ones....
Wordpress (self hosted)
As mentioned already with this platform you can have exactly what you want... 45,000 plug ins... thousands of themes. But you will need a Domain name, a hosting package, backups, and someone who knows how to recover your website if you are attacked. You will also need to learn the platform... not as intuitive as some. But you control your own website... it is yours.
Wordpress (hosted)
Same as above in flexibility and similar options but more restricted. You do not need hosting packages and less in terms of the security responsibility. It can be shut down by the wordpress company if you contravene their guidelines for use.
Blogger (also called Blog Spot)
Free to use and easy to set up. Far fewer options in terms of plugins and templates. Hosted by Google and all security taken care of by google. Little to no technical knowledge or support required. Expansion is limited and google can shut the site down too if rules are broken. You can be blogging in less that an hour from decision to start.
TypePad
Owned by an independent company Typepad is a paid for service with a high level of features and functions. Typepad has been around since 2003 and offers a comprehensive hosted service. It is a proprietary platform so it is what it is... One payment covers everything and if you wanted a low tech, high quality platform with low maintenance this is a good option.
Tumblr
More like a social network with your own blog built in Tumblr has a limited range of templates to choose from to style your own blog within the platform. Low cost, very easy to use and the bonus of being able to find like minded people within the social platform of Tumblr. A slightly different concept but if you wanted to be part of a network of bloggers and get up and running quick maybe a good option. No worries about security, backups and hosting.
Medium
A relative new comer to the Blog space Medium is a very simple platform focusing more on enabling people to write content rather than building a custom blog 'website'. Due to it's simplicity and speed of being up and running it has gained popularity with writers, journalists and bloggers. There is a social network built in which means you can track down like minded people. All followers of your blog belong to Medium... so you really are tied in to the platform... probably the biggest downside.
Squarespace, Joomla, Wix, weebly...
There are plenty of other options out there but to be honest the more choices you have the more difficult it is to decide. Each platform provides slightly different advantages and disadvantages.
I would probably break the options down into three main choices...