Organisations usually already have archives, and the priority, if they are worried about the preservation of their history, is to do something about those archives that they are sitting on. It's a nice flourish to run around collecting oral histories from aging individuals who have been associated with the organisation from the outset, or at least for a very long time, or to ingather bits of memorabilia. But it's not the most vital thing.
The core action point should be to talk to an archivist about the existing archives. It doesn't necessarily have to be an archivist whose repository might take the archives, just somebody who can give the essential advice about physical storage, what to keep and what to throw away, and someone who can advise on what repositories might be interested, from either local or thematic collecting policies.
The next thing is to get those archives into decent storage (and preferably not one of the more expensive commercial storage firms) rather than the coal cellar or the loft where pigeons have started roosting and to which entry is restricted to able-bodied persons who can manoeuvre up the rickety drop-down ladder and through the hatchway.
It is always possible that it is quite feasible for the archives to be retained in a secure and safe manner on site, catalogued on the premises (preferably by a qualified archivist, or at least with professional input), and made available for ongoing research by interested parties. In most cases this is likely to present problems (archives take up space which may well be at a premium, who is going to deal with researchers, etc) , and negotiations should be opened with an archival repository.
If an organisation wants its history to be reliably preserved, its records need to be in a secure store with appropriate environmental controls, and the intellectual control over what's there needs to be gained via cataloguing, or at least, an adequate inventory identifying what's there and where it is located.
Once this end has been attained, it provides a sound basis for all those other activities.