In starting a new blog, one usually has three basic choices in setting the blog up.
1.       Set the blog up on a third party hosted site like
2.       Set the blog up as part of your domain like
3.       Set the blog up on your sub domain like www.
It is generally agreed by SEO specialists that #2 is the best option. Making the blog part of your domain will show the search engines that your website is constantly adding fresh content.   Google tends to put a premium on content freshness and Google also tends to pay more attention to sites with constantly changing content. So a blog on your site takes advantage of both of those items.
Google has stated that having the blog on you sub- domain is treated the same way as having the blog on your domain, but many experts still advise that the latter option is better.
So what about a third party hosted blog? After all there are a lot of free choices out there and many users don’t have the option of inexpensively adding a blogging tool directly to their website.  This option can work well also.   But the real benefit doesn’t happen until you have established the blog and gotten some traffic.   2-3 posts per week and a little link building over a 8-12 week period should start to get your blog some traction. Then when you create text links to your main site, you should get some link juice benefit.   Also you can drive some of your blogging traffic to your main website.   
With a little link building and some perseverance, you can make your third party hosted blog a very effective marketing tool.