I'm currently reading The King's Ships Were at Sea (USNIP 1984), which covers the Royal Navy's activities from August 1914 through February 1915. I just got to the sinking of the HMS Audacious, and the book mentions that a number of photographs - and a "moving film" - were taken of the ship in her distress. Well, I wanted to see if by some chance that film was still around, so I did a web search. No luck on finding the film, but I did find a number of photos of the submerged wreck (only discovered in 1995) - and then I came across this webpage:
http://www.maritimequest.com
I would assume that a number of folks here already know of the site, but I figured it's worth mentioning - they have an extensive database of capital ships and for most of them they have photos posted as well. They go back, comprehensively, to the beginning of the 20th century, and have at least a few ships listed before that time - not sure how many, though, since there are so many ships listed there in total. But if you're looking for a pic of a warship from 1900 or later, chances are they have one (or more).
Note to MackP - I checked, and the earliest USS Texas they have photos of is BB-35. They don't have anything on BB-1.