You should upload your videos everywhere you can: YouTube, Facebook, Twitter, Vimeo. The more places your video lives, the greater the exposure. Google will not punish you for sharing your video across multiple places. Facebook especially is becoming a crucial platform to natively upload your videos.
As for which platform to use for embedding on your website or blog, we personally recommend Wistia to our clients. Videos embedded from Wistia will direct searchers to your website, rather than Youtube or Vimeo. They also have a lot of other analytics and business-focused marketing solutions.