Comment Um....tape??? (Score 4, Informative) 266
The fact that you haven't thought of tape makes me question how well you know the industry you're in, or how well-connected you actually are. Why can't you put your video files onto DigiBeta or similar? Tape stores well, and with a format like DigiBeta you're pretty much guaranteed compatability for at least 50 years+ (since there's so much TV back catalogue stored on tape, and there will always be a need by broadcasters to get to that content).
I don't want to come off as rude, but it just sound like you don't really know much about video production and archival, despite the fact you've chosen to produce video installations and artwork. You're not the first person in the world to do this kind of thing - there are established proceedures for dealing with and archiving video installation work. This still doesn't entirely solve your problem of storing your raw data, but since you specifically talk about .mov files I'm perplexed that you haven't already thought of tape.
I suspect you're going to get a lot of answers here that are wildly impractical for a gallery or go well beyond your means - but the fact is this: if a museum or gallery is looking to purchase your work, they should already have a curator who knows the medium. If they don't have a curator who can discuss with you the formats he/she would like the work in, the gallery probably needs to rethink what it's doing in the business!