Ideally I would like to show the actual advertising that the companies have used to market their games (ie posters, manuals, actual cartridges, released concept art, etc.).
I wouldn't want anything really created by me (or anyone i hire) as that does not show the history.
As for rebroadcasting, i would like to show actual gameplay, however not just anything found off of youtube as i already know the definitive legal standpoint on that. I would prefer to use footage that the companies themselves have released as promotional material.
Also, two little things to note, how much would companies approximately charge for licensing them in this capacity (since I am not using them in my own creation, but using them in an educational standpoint) and also would it be protected under fair use doctrine if I do not charge a fee to enter the museum?
If you legally purchase the items you wish to display in your museum, that is something you are allowed to do under the first sale doctrine and 17 USC §109(c) (
https://www.law.cornell.edu/uscode/text/17/109).
If you wish to show actual gameplay, this is also something you are allowed to do.
But, you cannot copy any material for use in your museum, and you cannot show video footage of any length that is produced by the game companies, without written permission and possibly a license from the companies to use the material. Licensing fees will vary, depending on the companies involved - and it is even possible that a company will not charge any licensing fee at all but rather donate material for display and use in your museum. The "of any length" can be a problem because short clips can often be permissible under a fair use exception to the copyright law, but determining what length the holder of the rights thinks is fair can sometimes be left for a court to decide. Therefore, you are smart to get permission for even short clips.
The major problem I see with your museum is in the advertising of it. You cannot use any rights-protected material in your promotional material that could lead a consumer to believe the rights-holder endorses or supports your museum or is in any way connected with your museum.
And, if rights-holders take exception to any of your uses of their material, you will need to defend your use. This can get costly.
Therefore, a careful review by an IP attorney in your area, and getting permission from the rights-holders whose material you wish to display, can be your best insurance in avoiding a lawsuit - although having liability insurance coverage for your museum is also a smart idea and recommended.
Your museum sounds interesting. I wish you good luck with it.