Chris, if you give the serial number I might be able to put you close to the year made. There are no records of these guns and just an estimate on how many made.
The grade would be stamped below the serial number. They were listed from 1-5 and 1 being the lowest grade made. The Quality 1 (grade 1) came with a straight stock and for $5.00 you could order a POW (Prince of Wales or half pistol grip). The gauges were 10 or 12 and the caliber was listed as 44-40 although there were many others. Yours is most likely 38-50 Ballard (circa 1876) or 38-55 Winchester for Ballard target rifles. (circa 1884). Metal butt plate is common on all.
Early Baker guns had W H Baker on locks. Later Smith-Baker guns had Baker Pat on locks and after 1883, L.C. Smith on locks. (only a few of these seen)