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On your own server, but stick it on a VPS in a different data center from the main site so that it's online when your startup isn't.

Any reason why self hosted blogs are preferred? Why should a start-up host and maintain a blogging software?

I know its not very difficult to do, but shouldn't a start-up focus on its core?

SEO. To fully realize the SEO benefit of inbound links you need to self-host.

You can just use a reverse proxy to get the seo advantages, without getting the security problems associated with self-hosting.

Hadn't thought of that, good point

Basically, having a blog at yoursite.com/blog is more SEO-friendly than something like blog.yoursite.com