What you have is a Winchester Model 1873 lever-action rifle. Chamberings included 44-40(44 Winchester or 44 WCF), 38-40 (38 Winchester or 38 WCF), 32 Winchester (32-20 or 32 WCF) and .22 rimfire short or long cartridges.
The number in front of the letter"A" is the serial number which includes the letter "A"
The Cody Firearms Museum in Cody, Wyoming has factory records which could be used to help date your firearm as well as confirm its authenticity for a fee.
For more information, get the book "Winchester Lever Action Repeating Firearms Volume 1 - The Models of 1866, 1873 & 1876" by Arthur Pirkle published by North Cape Publications, Inc.
You could also visit the Winchester Arms Collectors Association (WACA) website and go into the forum there - it's free and do a search for more information on 1873s as well as look at other examples and learn more about the history of these interesting firearms.
Try using the search engines and I'm sure you'll turn up a lot more information.