I quote part of the FAQ of GNU licenses below:
Is there some way that I can GPL the output people get from use of my program? For example, if my program is used to develop hardware
designs, can I require that these designs must be free?
In general this is legally impossible; copyright law does not give you
any say in the use of the output people make from their data using
your program. If the user uses your program to enter or convert her
own data, the copyright on the output belongs to her, not you. More
generally, when a program translates its input into some other form,
the copyright status of the output inherits that of the input it was
So the only way you have a say in the use of the output is if
substantial parts of the output are copied (more or less) from text in
your program. For instance, part of the output of Bison (see above)
would be covered by the GNU GPL, if we had not made an exception in
this specific case. .....
In what cases is the output of a GPL program covered by the GPL too?
The output of a program is not, in general, covered by the copyright
on the code of the program. So the license of the code of the program
does not apply to the output, whether you pipe it into a file, make a
screenshot, screencast, or video.
The exception would be when the program displays a full screen of text
and/or art that comes from the program. Then the copyright on that
text and/or art covers the output. Programs that output audio, such as
video games, would also fit into this exception.
If the art/music is under the GPL, then the GPL applies when you copy
it no matter how you copy it. However, fair use may still apply.
Keep in mind that some programs, particularly video games, can have
artwork/audio that is licensed separately from the underlying GPLed
game. In such cases, the license on the artwork/audio would dictate
the terms under which video/streaming may occur. ....
Can I use the GPL for something other than software?
You can apply the GPL to any kind of work, as long as it is clear what
constitutes the “source code” for the work. The GPL defines this as
the preferred form of the work for making changes in it.
This is answered by the third answer from the FAQ quote above, assuming we intend to use the GPL license to cover both software and video/ artwork.
All open source licenses (based on the Open Source Definition by the Open Source Initiative) allow copying, redistribution and sale verbatim. However, copyleft licenses require modified source to remain open.
"Encourage sharing and for what is free to remain free" is essentially what copyleft is all about.
GPL and MPL are copyleft licenses. I'm not sure if MPL can be applied to video or artwork or not, but GPL can be.
I think if you apply the GPL to your software and your source videos or artwork that is used to generate the output video, then it fulfills most of your open sourcing goals under a single license.
MIT and BSD are free, permissive licenses, not copyleft.