Hello, First let me state I am not a professional. You do have a very nice revolver there. Though you may already have perused it I would recommend this site
Smith and Wesson Model 2 Army Revolver
It is a good site that is interesting for the model 2 lover/collector. The type 3 is within the 3109-10121 range. These were constructed during the Civil War and there is a chance it was issued or a private purchase weapon used during the period. They have a database of serial numbers, check it, they were popular. Apparently Earl Van Dorn had a pair of 5" barreled ones and Sterling Price had a 6" piece.
A quick check of the gunsinternational.com website has model 2's listed for 990-1600 depending on condition. The lower price has about 40% finish with the higher price 90-95% finish. I don't know if they can sell at those prices but that's what they are listed for.
Are there any other markings? Many of the type 3's were marked on LH side of barrel S.Kittridge and Co. Cincinatti Ohio.
As my neighbor has stated you would want to check the assembly numbers etc. to see if it has all original parts and is not a mix of parts from different weapons. Sometimes a replacement barrel or other part may have been put on at a later date. This would lower the value.
Were there any other accouterments or such that came with it? It is possible to get a factory letter for it, as you probably already know. It would be well worth the small cost and might help with some type of provenance/chain of ownership. Have fun, show us more pics, and let us know of the results.