The attached link will take you to a brief history of the Baker Gun Company.http://www.bakercollectors.com/index.php?p=1_7_History-of-the-Baker-Guns
Blue Book of Gun Values
the best place for gun info would be cabelas gun library.
Wilmot Gun Company was a trade name made by Henri Pieper in Belgium c. 1877-1914.
Blue book of gun values
Made sometime between 1905 and 1931. They were made by the Baker Gun Company in Batavia New York.
Look in "The Ithaca Gun Company - From the Beginning"
UMC refers to Union Metallic Cartridge company. They are owned by Remington and only make ammunition not firearms.
You can find out @ when it was made/shipped and other data depending on what, if anything , has been published by the company.
Have you tried the Internet?
Try e-gunparts.com, gun shops, gun shows, want ads.
I posted a link in the related links section that may be of some help.
There is a lot of Information on the Baker Gun & Forging Co. They started in 1890 and made shotguns up to 1923. They made several different grades of shotguns. I suggest that you go to a book store and find a book called "2008 standard catalogue of firearms 18 edition" in it you will find several different photos of shotguns and listing of the different grades. All of them are valuable. look on page 104 for the information you are seeking.