If you have videos on your website, it’s worth spending some time considering the presentation. I’ve seen too many videos for my liking which are hosted on YouTube and left to recommend other “related videos” at the end, often including those from competitors. There are a number of ways of making YouTube hosted videos look more professionals, and a number of alternatives to YouTube.
It’s quite possible to host your videos on your own website, but I’d always suggest using a third-party specialist video hosting site, and displaying the video “embedded” in your site. Here’s some reasons why (written for WordPress users but applicable to all). There are many hosting sites you can use; some are free, some are not, but don’t just rush to the free services.
Even if you choose not to use YouTube, you’ll probably want to upload your video there too. People search on YouTube directly, and although Google would probably deny looking more favourably on its own video site, it’s true that YouTube videos do seem to perform well in Google searches.
If you are using YouTube, take care to set the video up properly and don’t just accept the default settings, especially for embedding. You can control whether the video plays automatically on your site, whether there are play controls present, and whether there’s a YouTube header bar. And yes, you can remove those “related videos” at the end. There’s a great article here if you want to investigate all the possibilities.