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
Look in "The Ithaca Gun Company - From the Beginning"
You can find out @ when it was made/shipped and other data depending on what, if anything , has been published by the company.
UMC refers to Union Metallic Cartridge company. They are owned by Remington and only make ammunition not firearms.
Made sometime between 1905 and 1931. They were made by the Baker Gun Company in Batavia New York.
Have you tried the Internet?
One can find plenty of information about gun shows on websites such as "Showmasters", "Cross Roads Gun Shows", "Gun Show Trader" or "East Man Gun Show".
I posted a link in the related links section that may be of some help.
Library, gun shop, gun shows, the internet