3rd party platform generally isn't the way to go if you mean a hosted version like Wordpress.com or Tumblr. Yes, Tumblr ranks well, so does blogger.com. But SEO is not a thing that is just on or off; it fact, the term is increasingly misleading as Google has enhanced it's engine so much that how you rank is primarily determined by only unique/quality content, social validation, and other's content on your behalf. Successful SEO is really just a matter of it being part of your company culture... good UX, developers who always consider the implications of what their doing to searchers, good PR/BD, content marketing, and business intelligence (by way of key word intel - easily done through Google Trends of Adwords).
So why not have a 3rd party hosted platform? Because it isn't your domain. If your business is on domain.com and you set up a blog on tumblr or domain.blogspot.com, etc. you aren't building and leveraging your businesses domain equity. "Can't I just use the paid version to have it live on my domain?" Yes, but no. It's still not yours and at the end of the day, you don't control 100% of the experience to ensure it's consistent with your business model... for example: being able to reduce bounce rates by having a custom blog UX that draws the audience further into your business, optimized by multivatiate testing. What does testing and conversion rates have to do with SEO?? Everything: SEO isn't a thing anymore, it what happens as a result of doing things online well. Bounce rate is one of the most significant factors determining where you rank.
Set up your blog on Drupal, Joomla, or WordPress CMS (not the hosted version - download it and install it on the same server as your businesses' website - NOT a subdomain!). Frankly, I'm being generous in referring to Drupal and Joomla - set your blog up on WordPress. 60% of the internet isn't wrong.
Want the easy way to do it? Check out http://wpengine.com
Upload a theme you love from ThemeForest.net
Install these plugins (for SEO):
All in one SEO