OneShot, the first thing to understand is that both shotguns basically do the exact same thing. The "Special Purpose" is just a marketing label that Mossberg puts on their catalog description really. The 590 comes in the 20" barrel length, and the A1 will give you the option of either the 18.5" or 20" barrel.
The 20" barrels are long. Obviously, 1.5" isn't a whole lot, but it can be noticeable. Moreso if you're getting in and out of vehicles or in very tight spaces. With the A1, they are also slightly heavier. Now granted in HD use you're probably not going to be carrying it long distances or for a long period of time. but if you should need to hold it one-handed, it gets more noticeable. The benefit to the 20" version is that you get 3 more rounds. May be important to you, may not.
The 18.5" barrels are a little shorter and lighter. They are still going to be the A1 heavy wall, so the weight savings won't really matter except when compared to the 590A1 20" model. You do have a 6 round capacity. You can get an extension for it if you want. On the plus side to the 18.5" model is that you can use the sporting barrels for an 835 on it. So you can have a purpose built defensive gun with a short barrel and then switch out a longer sporting barrel if you want.
Where that extra 1.5" length can make a difference is if you put a short LOP stock on the shotgun like the Hogue ShortShot or a cut down OEM stock. If you can take 2" off of the stock and then consider the 1.5" on the barrel, that's almost 4" of length gone.
The A1 package includes the metal safety, metal trigger guard, and heavy wall barrel. The metal safety is a nice feature. Mossberg safeties have a checkered history. The metal safety is a nice insurance policy. The metal trigger guard is another insurance item, but one that I don't think I've heard of being a problem. The heavy wall barrel is nice for steel environments, and for knowing that it will take pretty much anything you could ever do to it without denting. Of the three, I would say that the metal safety is the only thing I would absolutely want of the three on any 590 I would ever buy.
As far as customizing, I would say wait until you have the shotgun and shoot it a few times before you decide what to add to it, if anything. If you're using it for defensive purposes then consider what benefit anything you want to add has. If it enhances or creates the defensive capability of the shotgun, then get it. If it doesn't, or is for cosmetic purposes don't get it.
As a minimum for me a defensive shotgun should have a light and a sling. Beyond that I would consider adding a tritium bead and a means to carry extra ammunition. But before making that decision, get some triger time with it and ideally a class or two.