By default the iPad should export/share videos as .MOV by default. Most players will handle or convert that fine. If you email a video directly from Photos, thats what you’ll get. If you upload to a site using Safari, MOV files will probably work. If not the site should warn you that the file is incompatible.
Apps that allow you to share videos from the iPad will automatically convert it to whatever format that app and or site needs: Facebook, Twitter, etc.
You can import videos from the Photos app to an iMovie project and export the movie as an .mp4.
There are a ton of movie/video apps out there than can do all kinds of conversion editing tricks. Many one-trick ponies, and a few more sophisticated than iMovie.