Like everyone's grandmother, I am starting a blog. The blog is meant to support a company Web site. Keeping in mind that the mission of the subject blog is to enhance the company site's search engine rankings for a few choice keywords, I guess the essence of the question is: Which site will rank better? One with great content of its own, or one with many inbound links from another site (that is, the blog) that says, "Look at the great content that that other site has!" The "miserable failure" example from years ago would indicate that--at least back then--the second approach (blog on its own site) would do a better job, but then again those inbound links came from different sources. In the case of the blog, however, there's really only one "source," isn't there? So...what approach should rank bmh.com better for the phrase "bees make honey?" A site (bmh.com) with good content and lots of on-site blog postings (blog.bmh.com) about how bees make honey? Or a site (bmh.com) with good content (no blog, though) and a lot of inbound links from one off-site blog (bmhblog.com) that says that the site (bmh.com) has good content about how bees make honey?
I would use either a subdomain or subfolder to house the blog if you want to use this to help with your search engine rankings. A subfolder would probably be the best way to go, but don't do that on my opinion. SEO wise neither the subdomain or subfolder would be superior to one another, so it's a matter of personal choice.
I suggest only to create a blog on your own site by creating a subfolder, like thisisyourowndomain.com/blog. This is great tips in view of search engine optimization. Put fresh and related content and get inbound links for your blog. Both work will support only yoursite.
I would also like to suggest you to have your blog on your website itself and post useful and relevant articles in support of your services & products, and other related information, You can promote your blog separately with on page optimization and posting the same on blog directories. All the best.