What is the best strategy for playing a video embedded on a webpage to provide the optimal user experience?

Many websites that embed videos now seem to follow the trend of automatically playing them. I believe that facebook is one of these types of websites, but it is probably the exception rather than the norm. There have been other questions around whether this is a good UX practice, but I want to explore the question for what the best strategy is.

I think some of the issues involved are:

• Type of website - whether it is video-centric like Youtube or mostly text/graphics based
• Nature of video - whether it is advertising or content
• Mode of play - automatic, timed delay, manual
• Speed of connection - mobile data network or direct ADSL connection

Is the case where a video-centric website showing content on video using automatic play mode the optimal user experience strategy? Should other websites that do not conform to these parameters seek an alternate strategy in the interest of better use experience?