I've always preferred static blog engines myself, so consider that bias when reading these suggestions.

octopress/jekyll are great. frog is okay if you want a more minimal octopress or are more familiar with racket or bootstrap.

aesthetics are pretty blog-engine agnostic, although some engines make certain styles easier to emulate simply due to their defaults (frog uses bootstrap, for example). If you're intending to use an off-the-shelf theme it'll probably be easiest to just use the engine that theme calls for.

If you are familiar with a certain mark-up language, pick an engine that supports it out of the box. Most every engine has a language it prefers, so if you're already familiar with the syntax and language you'll reduce the burden of learning the already foreign software by choosing a familiar route as far as markup languages go. Don't let it be a deciding factor though--many of the more advanced/expansive engines support changing languages on the fly.

Also, consider your method of deployment. Octopress/jekyll excel at github or remote deployments over rsync, whereas frog has no deployment options and is best either paired with other tools or on the remote machine itself. (I use these three examples, but the broad point is that they all take different philosophies on the matter, and that should be considered amongst the hundreds of options that exist.)

There seems to be a paucity of good drop-in themes, paid or not, for Octopress/Jekyll. There just is no theming community like for Wordpress :-(

I would go WordPress and host at mycompany.com/blog for maximum SEO advantages.

Using Medium.com would work well for discoverability, although links to those articles would mean less SEO effect for your website, but more people would be able to find your articles.

If content marketing will be a key strategy, then you may be best served publishing articles on both platforms.

Is mycompany.com/blog preferable to blog.mycompany.com for SEO purposes?

/blog is preferable according to Moz.com - http://moz.com/community/q/moz-s-official-stance-on-subdomai...

From this video, I'd say no:

https://www.youtube.com/watch?v=_MswMYk05tk

Ghost seems very popular.

https://ghost.org/

If the blog is for your company, it's preferable to host it on your own subdomain, i.e., blog.example.com. However, a blogging platform is just fine for a personal blog.

It's trivial these days to set up and manage a static site, especially for a blog—check out Jekyll[1] or Harp[2] (or any other static site generator).

[1]: http://jekyllrb.com/

[2]: http://harpjs.com/

Postaic (http://postatic.com) isn't a traditional "blogging" platform per se, but I've seen a few people using it as a content posting platform. It looks like you can certainly use it as a blog platform (I don't think it has text editor that is as good as wordpress).

It's used more to create online communities and audience though. Maybe you might want to take a look at it.

The best free option I've found is to run Ghost, Buster, and Github-pages.

http://talalanwar.com/host-a-ghost-blog-for-free/

You said it's for your company so I would run your own Ghost instance on the companies subdomain and be done with it. Medium can be great for exposure but ultimately your posts will be more valuable on your own domain.

http://gohugo.io is great. It's secure and runs everywhere.

posthaven?