Hello, Mike -
1. I took the liberty of re-categorizing your question from Optics (binoculars, gun sights, lenses, etc.) where it landed, to Firearms.
2. I doubt most who volunteer to answer questions on Fixya.com are qualified to provide you a value for your rifle. For one thing, an appraiser would need to look and handle the rifle, which is a major challenge online. :) (Note: My now late father, a licensed auctioneer, used to sell the firearms of his friends who had passed away for their widows and I know he needed to look over all of the firearms in-person.)
3. As for the year your Winchester 1890 was manufactured, you are fortunate in that the Winchester Repeating Arms company provides a PDF document (you will need Adobe Acrobat Reader software (free) installed) listing the models of firearms and range of serial numbers and what year they were manufactured. This is the link:http://www.winchesterguns.com/content/dam/winchester-repeating-arms/support/faq/serial-number-reference/Winchester-Manufacture-Dates-by-Year-2012-Scanned-Documents.pdf
Easier than looking through the lists on the Winchester Repeating Arms document, though, the database offered by the website for Antique Guns and Collectible Firearms and Militaria Headquaters
(home page: http://oldguns.net/
), Winchester Dates of Manufacture:
I think you can figure it out. :)
4. First, your local public library may hold a recent book or two listing estimated values of firearms. One title which is updated regularly is The Blue Book of Gun Values. Note: Using your local public library and its collections represents your taxpayer dollars at work!
Second, read the questions and answers about gun appraisers here:http://forums.gunbroker.com/topic.asp?TOPIC_ID=311759
Second, you can conduct a search using your favorite search engine (Google, Bing, Yahoo, DuckDuckGo, etc.) using the following search phrase:
Third, the International Society of Appraisers provides a database which can be searched. This is the link:https://www.isa-appraisers.org/find-an-appraiser
Enter the word firearms in the search box.
The American Society of Appraisers offers a similar database:http://www.appraisers.org/find-an-appraiser
In the ASA Specialty search box (only), choose Firearms.
Personal opinion: To find an appraiser to value your rifle, I suggest you do not go to a firearms dealer, who may opt to purchase your rifle outright, since he / she may have a vested interest in the value of your rifle. Be prepared to pay a fee for an appraisal.