It's really bad practice to have a video start playing when a visitor lands on a page. For one thing, they might have opened it in a background tab and not even be looking at it, so it's a wasted effort. For a second, they might not want to watch a video, so it's somewhat rude to presume they will. For a third, they might already be watching a video or playing music, and having yours overlaid with someone else's is going to be extremely irritating - especially if they aren't even looking at your page. For a fourth, they might struggle with video – for example, where I work we have really crappy computer terminals that seize up as soon as you try to play any video or the page uses various kinds of slideshow, carousel or animation. And you're then stuck looking at it flick through frame by frame, a few seconds at a time, for at least a minute before the computer responds to your next click. And if it's your site that's made it do that, the chances I'll ever go back to it are absolutely tiny.
In terms of whether to have the video on your site or YouTube ... you've got to think about bandwidth, technology and professional presentation. From the point of view of professional presentation, it looks better to have the video on your own site than to be relying on a third party service most commonly used to show puppies falling off skateboards and pirating TV programmes. But you have to weigh that up against (1) the bandwidth costs of serving video from your own server, and (2) whether you have the technology available to you to create and embed video in a format that is accessible across different platforms and browsers.