First, there is no such thing as a model 1860 Sharps Military Rifle. On top of the barrel will be marked "New Model 1859" or 1863, or 1865. Which is it, and what is the start of the serial number(ie, C 102XX, 784xx, 877x, etc.).

Is the gun original percussion, with a nipple for a percussion cap, or has it been converted to use a metallic cartridge?

I own several M1859 and M1863 Sharps. All show obvious wear,consistent with use in service; my personal tastes exclude any creampuff specimens, as they never saw use during the war. Many of my collector friends agree with this selection, but there are a few folks who prefer near mint examples; your task is to locate one interested in your specific weapon. While you will have to pay a commission, I'd say the best way to get exposure of such a mint piece is to have one of the top auction houses sell it for you. Cowan's, Amoskeag, Rock Island; these auction houses have frequent offerings of top items, and have established mailings lists of most selective collectors.