Hi Eric,
There is a Devonport Dockyard Museum situated just inside Granby Gate (South Yard).
This Museum holds open days through the summer but I'm not certain of the frequency.
Just down from the Museum is the old ropewalk which is a fantastic building.
Also, close by, there is a working gallows for hanging French servicemen during the Napoleonic wars

(I was told that it was mostly used by the French officers, to hang French matelots).
I'm not sure what the Museum holds in the way of records though, it could be worth contacting Plymouth and West Devon Records Office to see if they have anything, if not, the Admiralty may hold some records.
The Museum is open during "Navy Days", the next one of which is due in 2008 but I have not heard confirmation of this.
Plymouth_Ian