Since you didn't say if you are right or left handed, I will give you the top two choices. As stated the Rem. 870, hard to beat. If it were me I would go with an Ithaca pump. I have both and use the Ithaca more for the shells are released out the bottom vs the side as all the others. Turkey, deer or predators use the 3" shells. One other feature on the Ithaca, the deerslayer model has a rifle barrel for slugs. As for the pattern of the pellets, this is defined by the barrel choke, not the gauge of the gun. A 12 ga with a full choke will hold a tighter pattern than a 20 ga with a modified choke. If the gun is fit properly and held tightly against you shoulder, the kick will not be felt. You can but a gun anyplace, but it takes a GOOD gunsmith to fit the gun right. Stocks come in many lenghts and drops, a stock that would fit me in lenght would be useless for you. This is because of the lenght of my arms and the way I look down the barrel to sight on the target. Either one would be a good choice. The gun I liked shooting the best as a kid was a JC Higgins
pump. For those of you youngsters, that gun was sold by Sears for $29.00 in 12ga, a little less if you got a 20 or 410 ga.