In Blender, you can use several types of video formats as textures. If you want to avoid any potential compatibility problems, I suggest the use of standard video files in containers, such as MP4 or MOV. For the codec, you should look for H264 for maximum compatibility and smaller sizes.

You can use other types of codec such as WebM or MPEG-4. As a rule of thumb, you can use the same formats that Blender can produce. Going in to the render options and the video settings will give you a list of all available formats and codecs.