The Mossberg 5XX series, Remington 870, and Ithaca 37 have all been purchased and used by the military in great numbers. I've shot dozens of military shotguns and I will tell you a steel receiver is what lasts through decades of use. They all shoot about the same and, once broken in, they all are just as fast and smooth to operate.
If you want a gun in military furniture then the Mossberb would be my choice. There are many accessories and options for setting it up as a military/police/defensive weapon. One negative for me is that it uses an aluminum alloy receiver. Since 1970 it has been made with twin action bars. Prior to that Remington held the patent on that. I do not enjoy shooting the Mossberg because the safety bites me. It cuts the web of my hand if I use a full wrap grip or jams my thumb if I use a four finger grip with thumb forward. It's inexpensive, and reliable. The plastic trigger guard and alloy receiver were designed to contribute to light weight but I would rather have the weight and a gun made of steel. It should be noted that the 590 has some improvements to increase robustness, particularly to reduce chronic breakage of locking lug pins. And the 590A1 is a beefed up version of the 590 with an aluminum trigger guard and a thicker barrel. Those were needed to reduce problems encountered with trigger guard breakage, barrel dents, and barrels bending. As a result, the 590A1 weighs a bit more than the 500 or 590. I believe it even weighs more than a similarly configured Remington 870.
If you want a gun for general hunting and shooting then the Remington 870 is a better choice. It has a long history of military use but civilians make up the vast majority of users. The 870 can be had with plastic or plain Jane wood but they are more often found with with beautifully finished checkered wood and nicely blued steel. They also come in various flavors of camouflage. There are models configured for Sporting Clays, Trap, Turkey shooting, waterfowl shooting, upland shooting, police and home defense. They are strong, reliable, slick operating and you will be able to find parts, barrels, and chokes at almost any place that sell guns. Remington held the patent for twin action bars and Mossberg copied it as soon as the patent expired. They say imitation is the greatest form of flattery.
If you want a gun with hunting first and foremost in your mind then the Ithaca 37 would be a great choice. It feeds AND ejects from the bottom. That leaves the sides of the action walls solid and helps keep water and debris out of the internals as you hunt the woods. The design has been around since 1937 with some improvements made in the 1980s. When it comes to swinging, point-ability, and getting on a bird, I find the Ithaca my favorite. The Ithaca was used by the military for many years and is extremely rugged but you can't drop a round directly into the chamber like you can with the Mossberg or Remington. Because it lacks that feature it would not be my choice for defense use. However, I would choose it over the others as an upland gun for pheasant, quail, grouse, etc. When it comes to slug and buckshot deer hunting guns, well, Ithaca wrote the book.