On the 590 series, I like the following-
Vang safety, or the ETA safety. The Vang is well done, and offers a little more purchase than the stock unit. The ETA is wider, and has a great profile that seems to mesh with my thumb perfectly.
Short LOP stock or Speedfeed magazine stock. The Speedfeed has been improved over the early models that would push the recoil pad out away from the stock if the tubes were loaded. It offers a way (but not a convenient way) of carrying extra ammo on the shotgun, especially if you don't have a sidesaddle. The short LOP stocks are usually a better fit, particularly to those that want to shoot more squared up.
Sidesaddle of some sort. The TacStar has never given me a problem since I started using them back in the early 90s. The Mesas are good units, but it is important to load the rounds in brass up if you don't want to leave a trail of shells behind you during movement and firing. If you leave the rounds in the carriers this will happen regardless of which one you use at some point. If you stow your shotgun in a vehicle it will happen quicker. If you take them out after a shift or whatever then it will slow down and possibly eliminate this. The elastic units like 3 Gun Gear and Vang seem to work well regardless of the direction you put rounds in.
A sling of some sort. Yes, even on an HD gun. On pump guns I like a simple GI two point or similar. I'm trying out an OSOE bungee sling right now to see how I like it. The adjustable two points are good slings as well. I don't care for the three points, and a single point is more comfortable and capable on an SBS usually depending on how you have it mounted.
Lights are essential, especially if it is for HD and you live with someone. Target ID is a good thing, and if you think that I'm saying to run around with the light on all the time and that it is a beacon back to me please go get some low light training. The Surefire weaponlights are ideal, but not everybody wants to lay out that kind of money. No problem with that, there are a variety of ways to mount a light. Just don't go with a MiniMag, and cheap lights tend to be that way for a reason. That said, there are some very good lights for not a lot of money.
For sights, I like the Mossberg GRS kit if you want something like that, and an XS Big Dot tritium bead if you want a bead.
The hi-vis followers like those offered by Vang and S&J Hardware are good. Couple it with a Wolff spring and your feeding will probably not have a problem.