Let's begin with what you don't need. You don't need an extended magazine. Your application doesn't benefit from rifle sights. You don't need a very long barrel. You don't need a pistol grip stock.
The important considerations are as follows. Gun fit is very important, not only does it provide a intuitive relationship between eye, bead, and target, a gun that fits correctly doesn't feel like it kicks as hard as one that is too long. A wood stock is beneficial to the extent that its easier to shorten or lengthen than a plastic stock. A shotgun needs a quality recoil pad, and if the length of pull has to be changed to suit you anyway, don't skimp on the cost of a high quality pad. Interchangeable chokes are beneficial, and make the gun more versatile, whether shooting skeet or pass shooting geese. A 26" barrel provides a nice balance between a gun that points well and that's still fairly compact, here 24" can feel a bit clubby and 28"-36" can feel like a lot of gun. You need a bead you can see. In this respect, an XS Big Bead is something you can install yourself; it just glues on over the factory bead, and is much easier to see. A sling can be beneficial, particularly when the gun is used in wet conditions hen you would rather not put it down. Furthermore, the use of a sling is less fatiguing than having to carry the gun in your hands for hours at a time.
Action type has much to do with personal preference, but here are some things to consider. Semi-autos have the advantage of a solid forend that doesn't flex or twist in your grip. In the case of gas operated actions, it can reduce the recoil sensation, but not with recoil operated actions. And obviously you can fire successive shots without moving your support hand. You can't short stroke a semi-auto, and it will run reliably provided you keep enough mass behind the gun, particularly recoil operated guns, although you can't really expect light target loads to cycle as well as full powered loads, although the "B" guns do reasonably well in this respect.
Pump action guns are usually less expensive than semi-autos, yet have a similar appearance and feel and weight, load in a similar manner, and can use similar accessories. The pump is generally believed to be more reliable, but this is a myth that needs to be put to bed. A quality semi-auto is equally reliable compared to a pump of similar quality when full powered ammunition is fired. The pump action though is usually easier to clean and maintain. Aftermarket barrels are available for many pump and semi-auto shotguns, if that is something you consider advantageous.
O/U and SXS guns are another option, and while they are a low cost option, and occasional an expensive target gun option, single barrel guns are not as useful. At one time double barrel shotgun came with fixed chokes usually F-M or M-IC, and occasionally M-M or IC-IC. Happily, quality double guns like their repeating brothers are becoming available with screw in chokes. The big advantage a double has is shorter overall length when the barrels are equal lengths to a repeating shotgun, or it can have longer barrel while the its the same length as a repeater. The double breaks don into a very compact package for transport or storage. It is simple to clean and maintain. My preference is a double trigger gun, but single trigger guns are available; recoil resets the trigger; as you can imagine, should light loads be fired, or a less than text book hold that fails to put enough mass behind the gun, could cause the trigger not to reset.
Occasionally one comes across a bolt action shotgun. These used to come in a couple of guises, the first were inexpensive, box magazine fed guns usually made by Savage or Mossberg; I haven't seen one in quite some time now. More common today are quality bolt action shotguns intended to be used in shotgun only areas, as short to medium range big game rifles. Typically these have receivers that readily allow the mounting of optics or receiver sights, and typically have rifled barrels. These guns are specialized, and are not particularly versatile beyond their application as big game rifles.