The site we're developing is free as in free-to-view, not free to develop
Just to summarize our experiences and where we got to, in case someone is searching and this comes up.
The issue with YouTube is that we can't remove the logo; we generally use YouTube for most video content because of the incoming SEO advantage. YouTube has a general tackiness issue, by perception, and this industry is all about dignity etc, so it's unfortunately probably inappropriate to use YouTube even if the videos are embedded.
We've ended up using Vimeo, which does allow you to un-brand the player for a reasonable price, and just magically works beautifully and well on everything - iDevices, all browsers, the lot. Turns out there are a lot of sites around that do this well, which is something obvious that probably should have occurred to me! The advantage of using an established commercial platform for video delivery is that they track the video standards and will do what's needed to support emerging devices and new standards over time. And we don't have a high view rate or a high upload rate.
There's a great list here of possible video platforms: http://stackoverflow.com/questions/1060020/video-hosting-upload-api-service-for-small-business-other-than-youtube
We did try the Contus HD FLV player - not as robust as we'd hoped - it looks pretty, but doesn't cope with a lot of video types and they carefully refrain from mentioning the types they support in detail on their site. It also doesn't work on iDevices without an HTML5 wrapper - if I'm paying for a player I'd like it to solve those issues clearly and well, instead of in half-documented fashion. (For instance, unsupported video types generated a player message "No such video"!) This player was a disappointment and I'd avoid it based on our experience (early 2011).