To learn about sharing videos, including the options you have, please see this You Tube Help Doc:
YouTube Help: Embed videos & playlists
For any YouTube video that you want to embed on your website, you can disable the ads (that appear on YouTube videos).
You can also make your video auto-play, so that as soon as the page with your video opens, the video will start playing.
If you are going to have your video auto-play, we recommend not adding music to your video.
This needs to be done from your YouTube account.
From this help video:
Turn Off Ads on YouTube Videos
(Published on Jun 26, 2015)
As of September 25, 2018, YouTube no longer offers this as an option.
Titles, channel information, and related videos are an important part of YouTube’s core user experience, and this change helps to make the YouTube viewing experience consistent across different platforms.
However, YouTube goes on to mention that you will have the option of specifying that the related videos shown in the player should be from the same channel as the video that was just played.
See this video for How To info:
How To Make a YouTube Video Autoplay
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