J.C. Higgins was a trademark used by Sears, Roebuck, & Company between 1946 and 1962 for shotguns and rifles manufactured by a variety of suppliers. One of my cross-references states that your J.C. Higgins Model 20 12-gauge pump-action shotgun was actually manufactured by High Standard of Connecticut, and corresponds to their Model 200. Unfortunately, this reference does not list any values.
Another reference states that the Sears Model 20 corresponds to the High Standard Flite-King (also a pump-action shotgun, available in 12, 16, 20, 28, and .410 gauges). If this is the same shotgun, then the approximate value for a field-grade gun might range from $165 to $110, depending upon condition.
Regarding the 2.75" chamber reference: this refers to its length, and not to a specific specific shot or load size. For many years the "standard" American shotshell (in most gauges) was 2.75" in length before crimping.
For a quick primer to help you understand the best load for your particular shotgunning needs may I recommend that you visit your local gun shop and pick up copies of the product guides published by the ammunition companies (Winchester, Remington, etc.) While you're there, you might have the shop's gunsmith inspect your heirloom (paying particular attention to the barrel--no bulges, dents, or excessive corrosion) to make certain that it is safe for you to shoot.
Welcome to the ranks of the scatter-gunners! Our world is different from that of the rifle-shooter because a shotgun is pointed, not aimed, and our targets are typically moving; however, I believe that you will find it to be enjoyable.
Good luck, and good shooting!