Not meaning to sound snarky, but look at the muzzle. It should be easy enough to roughly measure.
If you have a 9mm round, stick the bullet in the muzzle, if it goes in nearly to the case, its a 9mm, if it only goes 1/3 of the way in (or so) its not a 9mm.
I think my Luger book is buried behind the Christmas tree, so I can't help with the markings right now.
make a list (nice clear pictures, if possible) of all the markings on the gun, and someone here should be able to id it fairly well.
Luger serial numbers run in blocks, starting over with a letter suffix, so the plain digits alone are not a lot of help, without a letter, means the first production block of that year, usually.
I think the 1920 commercial guns were in both calibers, but until I dig out the book, am not sure, sorry, not a Luger experten.