Uploading audio and video files

Audio or video files should be uploaded in the standard WordPress way using the WordPress Media Library (see the Media link on the left of the admin page). When editing a post you can also access the Media Library and upload a file by clicking on the Select file button in the appropriate area of the page.
Audio players are inserted behind the scenes by constructing an Audio shortcode (https://codex.wordpress.org/Audio_Shortcode). Since .mp3 files are supported across all browsers, that’s the only audio file format that you need.
Video players are inserted behind the scenes by constructing a Videojs shortcode (https://wordpress.org/plugins/videojs-html5-player/). Videojs creates HTML5 video tags from these shortcodes. There was a time when different video file formats were needed for different browsers, but now according to my reading of the browser compatibility chart at https://developer.mozilla.org/en-US/docs/Web/HTML/Supported_media_formats, H.264 mp4 video files are now supported via the <video> tag in all major desktop and mobile browsers, despite being patent encumbered. Therefore I don’t think you will run into any problems using just this video file format. However, the Mozilla chart should be your reference here.
The video will take up the available horizontal space excluding the right sidebar, with aspect ratio preserved, so you don’t need to be particularly concerned about the precise dimensions of your video.