Much that is old and scarce, or downright rare, also has zero demand and therefore no significant worth. Revisit the three parameters for worth: (1) fame in composition, (2) social/historical interest, (3) artistic merit in graphic design. Rarity without demand is the same as a piece in terrific condition but lacking demand. It has very little worth.

United States Zouave Cadets (1860)
Mendel lithography, Chicago

“If it has a pictorial illustration and dates from 1850, it must have worth.”

No, not necessarily. If no one can be found who’s interested in purchasing the worth is debateable. There are many mid-century sentimental songs that tell no story of significance and for which there is simply no demand. 

“A song with a gorgeous melody and excellent lyrics must have some value.”

Maybe, to the musician who reads music, but not necessarily to the sheet music collector. What, of significance, can be brought out about the piece? What place did the composer have in musical history? What does it say about the society? What story does the song tell, or what does the image on the title page suggest? What do you know of the music’s scarcity, its historical connection?

“Do you appraise collections?”

No. I do not do appraisals. I am happy to comment about relative market scarcity on any item, such as my experience as a collector of a dozen years can attest to. I am not a national ranked expert who has spent a lifetime viewing inventory and market conditions. I do have an excellent library on 19th century music publications and can assist with dating and information on composers and music illustrators, which is my area of authority.

“What are the key online resources in this field?”

American Antiquarian Society - The American Antiquarian Society (AAS) is an independent research library founded in 1812 in Worcester, Massachusetts. The library's collections document the life of America's people from the colonial era through the Civil War and Reconstruction. Collections include books, pamphlets, newspapers, periodicals, broadsides, manuscripts, music, graphic arts, and local histories.

The Lester S. Levy Collection of Sheet Music at John Hopkins University - The Lester S. Levy Collection of Sheet Music consists of over 29,000 pieces of American popular music. The collection spans the years 1780 to 1980, but its strength is its throrough documentation of nineteenth-century America through popular music. The collection is especially strong in music spawned by military conflicts from the War of 1812 through World War I, and minstrel music is also well-represented.

Sheet Music Consortium - The Sheet Music Consortium is a group of libraries working toward the goal of building an open collection of digitized sheet music using the Open Archives Initiative:Protocol for Metadata Harvesting (OAI:PMH). Harvested metadata about sheet music in participating collections is hosted by UCLA Digital Library Program, which provides an access service via this metadata to sheet music records at the host libraries.

Harvard College Library Online Resources for Music Scholars - Harvard College Library provides links to a number of sheet music specialty sites.

“What are the key publications in this field?”

The following are the books that have held the highest regard among veteran collectors of ‘first epoch’ American popular sheet music. Some are valuable for music research, some for illustrated examples.

The Lure of the Striped Pig – David Tatham, Imprint Society, 1973
The Handbook of Early American Sheet Music – Harry Dichter and Elliot Shapiro, R.R. Bowker Co., 1941
Handbook of American Sheet Music – Harry Dichter, Dichter published himself several volumes, 1947-66
Picture the Songs – Lester Levy, Johns Hopkins University Press, 1976
Grace Notes – Lester Levy, Oklahoma University Press, 1967
Flashes of Merriment – Lester Levy, University of Oklahoma Press, 1971
Patriots, Politicians and Presidents – Vera Brodsky Lawrence, Macmillan Publishing Co., 1975
Strong on Music – Vera Brodsky Lawrence, University of Chicago Press,     3 volumes, 1988
The Book of World Famous Music – James Fuld, Crown Publishers, 1966
A Pictorial Bibliography of the First Editions of Stephen C. Foster – James Fuld, Musical Americana, 1957
Bibliographical Handbook of American Music – D.W. Krummel, University of Illinois Press, 1987
The Singing Sixties – Willard and Porter Heaps, University of Oklahoma Press, 1960
Singing the New Nation – E. Lawrence Abel, Stackpole Books, 2000
California Music Covers – The Book Club of California, 1959
The Color Explosion – Jay T. Last, Hillcrest Press, 2005
The Star Spangled Banner (Issued Between 1814-64) – Joseph Muller, G.A. Baker and Co., 1935
The Star Spangled Banner – Oscar Sonneck, Government Printing Office/Washington, 1914
Bibliography of Early American Sheet Music (18th Century) – Oscar Sonneck and William Upton, Library of Congress, 1945
Secular Music in America (1801-25) – Richard Wolfe, New York Public Library, 3 volumes, 1964
Early American Music Engraving and Printing (1787-1825) – Richard Wolfe, University of Illinois Press, 1980
Suffragist Sheet Music – Danny Crew, McFarland and Co., 2002
Presidential Sheet Music – Danny Crew, McFarland and Co., 2001
New York: Songs of the City – Nancy Groce, Billboard Books (Watson-Guptill Publications), 1999