"tighter spray" or pattern, is affected by the choke, or the shape of the end of the barrel where the shot leaves the gun. There are different chokes you can get to give the pattern you desire at the distance you want. You can take a sheet of drafting paper, or newspaper or what have you, and hang it up somewhere safe for shooting and pace off thirty yards, sixty yards, or what distance you want to get a good pattern, shoot the paper, go up and look at it and see if the majority of pellets are around two inches apart, or to see if they tend to cluster to one side, or are WAY too dispersed to be effective against game. I prefer a vintage Ithaca 20 ga. just has a good feel to it. The amount of kick depends on the pressure of the load you are shooting vs the mass (weight) of the shotgun. There are countless recipes for custom shot shell loads that are optimal for a certain gun or pattern at a certain distance, or which travel faster, stay tighter pattern, produce less kick but travel as fast as a harder kick producing load. I assume you will be buying over the counter shells, so that is a moot point, other than to let you know there is a lot more to it than 12 or 20 gauge. So, type of shotgun, type of choke, and type of load in the shell, shock absorbing pad, making sure it has the right length of pull and is a balanced gun that you don't have to use all your energy to keep the barrel up all add up to whether or not you are going to have fun when you go hunting.
PS I don't own a shotgun but I used to shoot clays a few years ago with a borrowed gun and a guy that knew a lot about shotguns, loading shells, special loads. He had a great one he called his "powderpuff" load and it barely kicked at all, but it could pulverize and disitegrate a clay at any distance. I wish I had the recipe now.... Now look what you did. I wanna go shoot some clays... PLOW! (puff) woo hoo!