I've posted about that a few times over the last few years...
It really is pretty cool.
It's been YEARS since I've been there though. Has it moved, or is it still in the basement of the city building? (thought it was going to the new museum on the far south side of town on 35?)
Anyhow, last I was there, the cataloging system / display cards on the firearms was absolutely horrendous.
Typed out text (often quite minimal) on copier paper, then cut into squares and pinned to the backing.
If I lived a lot closer, I'd volunteer my time to help preserve, research, and better display the pieces.
That said, I doubt that it's the world's largest... Probably in the top 1% largest private collections. As far as oldest: Who knows. I do remember that the newest firearm in that collection is still quite an antique by today's standards.
If you're interested in another FANTASTIC firearms museum, head to Chickamauga and Chattanooga National Military Park. Go to the park office and go into the Fuller Arms Collection. It is, simply, absolutely amazing.
Almost pristine examples of EVERY type of rifle ever shouldered by an American from the Revolution, through the civil war (Confederate & Union examples), up to and including WWII. It's stunning.
It is in the museum on the south side of town. Decent amount of cars in the museum for its size. I haven't been in a few years, but it is well worth the trip.
My guess is that because they've not been stored in a humidity-controlled environment anyhow... There are indeed lots of cool things there, lots of old things, too. But it's not like the collection is chock-full of rare & pristine pieces.