YouTube is the second largest search engine, owned and powered by Google, the first largest search engine. This means that you should get a bit of a boost when you upload videos to YouTube.
I suggest linking videos from YouTube to your website whenever possible, rather than uploading videos to your website, because it will enhance your SEO.
Search engines can’t index video content, but they index your titles, descriptions, tags, closed captions, and transcripts. Please note that search engines cannot index open captions, which are burned onto the video file. Closed captions are uploaded as a separate file, in a search engine-friendly format.
YouTube has very few restrictions on videos (content, length, etc) and can accommodate a wide variety of formats. They offer a captioning service but it is reported to be buggy. Most professional videographers/cinematographers add their own captions before uploading to YouTube.