Very nice idea. There are already a few physical computer museums in existence so it could be a great idea for you to visit them first to gain ideas about how your project could be approached.
Are the machines intended to be hands on working examples of each one? Or just static display case examples of the hardware? And what sort of information and displays are you considering?
Did you visit the History of Video Games Exhibition that originally toured a few years ago? I saw it as the Barbican centre in London when it was first on, and it was later a permanent exhibition for a few months at the London Science Museum before beginning a tour around the world. That was a very nicely designed and setup exhibition with working examples of many of the systems on display, with hands on games that visitors could enjoy for many of them. They also handled the timeline of video games very nicely.
There is also an Arcade machine museum near Portsmouth. This has over 100 cabinets and they get cycled regularly to display as many of them as possible. The unique thing with this museum is that all of the cabinets are owned by different people who belong to the museum as a kind of owners club. This could be an interested approach to be able to get as many machines (especially rarer ones) into an exhibition space.