I believe that your Sears shotgun is a Winchester model 37A shotgun that was made for Sears Roebuck And Co,.
http://www.histandard.info/PDF/Sears%20Shotguns.pdf
sears roebuck and company
The Sears Roebuck Model 300 12-gauge shotgun with serial number 273521160 was manufactured in 1964. This shotgun was produced by the High Standard Manufacturing Company for Sears, Roebuck and Co. It is part of a series of firearms sold under the Sears brand during that era.
Its a Sears branded Mossberg 500.
The value of a Sears and Roebuck 12 gauge shotgun model number 281512651 depends on its condition. This gun in excellent condition is valued between 100.00 and 135.00 as of 2014.
The Sears Roebuck 12 gauge Model 583.606 was produced in the early 1970s. Specifically, it was manufactured between 1971 and 1973. This shotgun was made by the High Standard Manufacturing Company for Sears.
http://www.histandard.info/manuals/sears/pashotguns/index.html
1952 by High Standard for sears& Roebuck
$49.95
Winchester 1200
http://www.histandard.info/PDF/Sears%20Shotguns.pdf