Start with Tumblr. Write 10 high-quality blog posts, that get 100 readers a day. Then if you're not happy with Tumblr, think about changing.
Any blog platform can use Disqus, so that opens up the participation. Tumblr has the share/reblog controls for Tumblr members, so they can share your posts easier. Any blog platform can have Facebook/Twitter/Google share controls.
The next problem is your identity. If you host your own blog solution you can have it on a url like yoursite.com/blog or blog.yoursite.com
Tumblr also supports custom subdomains, so you could use blog.yoursite.com
The next problem is uptime -- Tumblr frequently has issues with uptime in my experience. On the other hand, if you're having uptime issues with your own site, it might be better for the blog to be hosted somewhere else so that you can let people know what's going on