Audio, Video and Animations
Simple animations can be done with animated GIF files - the use of these is chiefly confined to older-style advertisements and tacky clip-art.
Serious animation on the web used to be done with Adobe (previously Macromedia) Flash format (SWF files), and many still have the Flash browser plugin in their (desktop) browsers, but Flash is famously not supported by the iPhone and iPad, and because the built-in (HTML5 and Javascript) tools of modern browsers are much more powerful and capable, it has been in decline for some time.
Audio
This is likely to be more common than video on most church websites: talks / sermons / Bible Study expositions are the most obvious candidates. However you record the talk, make sure that the file is in MP3 format before you add it to your website. It's a de facto universal standard, and it's compact and efficient. (To be as compact and efficient as possible, make sure you make the files as mono rather than stereo.)
If your recording needs converting to MP3 format, a program like Audacity (which is a free download) will be needed.
You may set your audio files up as podcasts, or you may simply place them on your web pages. No special player is needed, as web browsers now have this built-in.
Video
No special player is needed for video any more either, although instead of hosting video on their own websites, many simply load their videos to Youtube or Vimeo and use the Youtube/Vimeo players on their web pages. This is often a good option.
Video is another thing which used to be formatted to be compatible with Adobe Flash (as FLV files), but now non-proprietory formats (typically OGG, MP4, WebM) are used.
Last updated: April 2017