I think that for most people the 590, which is the souped up 500 and not the mil-spec 590A1, is the best bet for most shooters.
It has the heat shield, which is a practical addition to a 500, and the bayonet lug, which is not really practical at all but provides some fun if one wants. Putting a heat shield on a 590A1 means going aftermarket and DIY.
The 590A1 is HEAVY. The thick walled barrel offers no particular advantage to the civilian shooter. As noted, it was to make the barrel more resistant to accidental shipboard dinging, where one might KERRANG!!! the thing off of a watertight door or its opening whilst running full speed. The 590 can use any barrel that fits a 500. It remains lighter and handier than the 590A1 when fitted with a sidesaddle, a lighted forearm, or other added weight.
The 590 is blued rather than parkerized. Whether that is an advantage is a matter of taste.
To my mind, the only reason to get a 590A1 are to get the 8+1 capacity of the 20" gun or to get the ghost rings for an affordable amount. The sights alone are a good deal of the markup difference if the price to acquire them separately is a reliable indicator. I only see a GRS setup as desirable for a longer range slug shot capability, again something that a sailor or a Marine might have more call for than any civilian buyer.
Leave the gun, take the cannoli.