Hi Esme,
I have worked with institutions who have installed compact shelving from a number of different vendors. One I’ve seen a lot is SpaceSaver (http://www.spacesaver.com/markets/museum-storage/archive-storage-solutions/). Rackline is another (http://www.rackline.com/product-category/museum-storage-display-shelving/). Most places should offer a consultation to provide you with an estimate. However, one of the best ways to decide which company to go with would be to ask an institution with a collection of a similar size and type to yours which storage system they use, and whether they are happy with it. That will usually get a pretty honest answer.
University Products and Gaylord sell flat files, standard shelving, and some carts but do not sell compact shelving.
RE-org is geared toward museum collections, but still has some helpful information for storage planning: http://re-org.info/