Ask HN: Where to host video for landing pages

I am just in the process of creating a screencast/product intro for a landing page but don't know where to host it.

Should I host it myself or with a provider? Which provider is good? Are there any good tools to track the views of the video and maybe at what time people stopped watching?

I would think having a YouTube logo or something similar on the video looks unprofessional, but maybe it also increases conversions? Is there any data about this?